November 7  11, 2011
Dutch
 Japanese Workshop
Analysis of nonequilibrium
evolution problems:
selected topics in material and life sciences
Summary
Common challenges exist in both material sciences and life sciences in regard
to obtaining and understanding macroscopic descriptions of phenomena. The
multitude of examples is vast and can be found in a variety of places (molecular
and biophysical chemistry, reaction kinetics and material science, as well as in
evolutionary, molecular biology and ecology...)
The challenges are generally twofold: On the one hand one wishes to find
accurate description of the microscale, while on the other hand, having in view
certain microscale dynamics (close to micro phase transitions), one wishes the
basic understanding over much larger scales. The second challenge is the one we
wish to touch with this workshop.
This meeting wants to bring together Dutch mathematicians working in the
analysis of Partial Differential Equations (PDEs) with direct applications to
material and life sciences together with overseas colleagues, working in the
same field, stemming from fife distinct schools of Partial Differential
Equations.
Regardless whether we consider a piece of metal or concrete material, or a
biological tissue, or a group of agents, the main keyword of the meeting is
“Localizing and Understanding NonEquilibrium Phase Transitions”.
Specifically we will address analytic aspects of nonlinear systems of PDEs
arising particularly in modeling the macroscopic behavior of materials such as
shapememory alloys, porous materials (e.g. concrete), biological membranes, or
chemotactic motion of agglomerated populations.
The discussions will be not only around typical analysis topics like
wellposedness, specific limits (e.g. fastreaction asymptotics, largetime
behavior, homogenization), nonlinear micro/macro transmission conditions,
coupling mechanics equations with thermal and chemistry models, but will also
include the analysis of hybrid systems  where discrete (microscopic)
interactions, capable to emerge welldefined macroscopic patterns, are coupled
with phenomenological macroscopic descriptions.
This meeting wants to be the continuation of the Lorentz Center workshop “PDE
Approximations in Fast ReactionSlow Diffusion Scenarios” (1014/11/2008,
organized by T. Aiki, D. Hilhorst, M. Mimura, and A. Muntean), of the more
recent workshop: “4th EuroJapanese Workshop on Blow Up” (Lorentz Center ,
611/09/2010, organized by J. Hulshof et al.) as well as of two special sections
on PDEs in Material Sciences (Arlington, USA, 2008) and (Dresden, Germany, 2010)
under the umbrella of the AIMS (American Institute of Mathematical Sciences) –
DCDS (Discrete and Continuous Dynamical Systems).
The journal – DCDS Series S (Discrete and Continuous Dynamical Systems) has
agreed to publish the best original contributions presented in our workshop.
Organisers
Dr. Adrian Muntean,
TU Eindhoven,
a.muntean"at"tue.nl
Prof. Dr. Joost Hulshof,
VU Amsterdam,
jhulshof"at"few.vu.nl
Prof. Dr. Toyohiko Aiki,
Gifu University,
aiki"at"gifuu.ac.jp
Prof. Dr. Nobuyuki Kenmochi,
Bukkyo University ,
kenmochi"a"bukkyou.ac.jp
Speakers
Aiki 
Toyokiko 
Gifu University, JP 
Akagi 
Goro 
Kobe University, JP 
Bouwe van den Berg 
Jan 
University of Amsterdam, NL 
Crommelin 
Daan 
CWI, NL 
Diekmann 
Odo 
Utrecht University, NL 
Evers 
Joep 
Eindhoven University of Technology, NL 
Fan 
Yabin 
Eindhoven University of Technology, NL 
Fukao 
Takesi 
Kyoto University of Education, JP 
Harada 
Junichi 
Waseda University, JP 
Hemelrijk 
Charlotte 
University of Groningen, NL 
Ishiwata 
Tetsuya 
Shibaura Institute of
Technology, JP 
Ito 
Akio 
Kinki University, JP 
Kano 
Rissei 
Kinki University, JP 
Kenmochi 
Nobuyuki 
Bukkyo University,
JP 
Kumar 
Kundan 
Eindhoven University of Technology, NL 
Kumazaki 
Kota 
Nagoya Institute of Technology, JP 
Nagase 
Yuko 
University of Crete 
Nakano 
Naoto 
Hokaido University, JP 
Nolte 
Robert 
VU Amsterdam, NL 
Merks 
Roeland 
CWI
Amsterdam, NL 
Murase 
Yusuke 
Meijo University, JP 
Ohtsuka 
Takeshi 
Gunma University, JP 
Otani 
Mitsuharu 
Waseda University, JP 
Peletier 
Mark 
Eindhoven University of Technology, NL 
Pop 
Iuliu Sorin 
Eindhoven University of Technology, NL 
Prokert 
Georg 
Eindhoven University of Technology, NL 
Rademacher 
Jens 
CWI
Amsterdam, NL 
Redig 
Frank 
TU Delft, NL 
Sawada 
Okihiro 
Gifu University, JP 
Shirakawa 
Ken 
Chiba University, JP 
Stojkovic 
Igor 
University of Leiden, NL 
Suzuki 
Takashi 
Osaka University, JP 
Tasaki 
Souhei 
Osaka University, JP 
Fatima 
Tasnim 
Eindhoven University of Technology, NL 
Wakasa 
Tohru 
Meiji University, JP 
Watanabe 
Hiroshi 
Salesian Polytechnic, JP 
Zaal 
Martijn 
VU Amsterdam, NL 
PROGRAMME
Monday November 7
Tuesday November 8
Wednesday November 9
Thursday November 10
Friday November 11
Abstracts
Toyohiko
Aiki (Gifu University, Japan)
Largetime behavior of a free boundaru problem describing concrete carbonation
A mathematical
model for a concrete carbonation problem has been proposed by Böhm and Muntean
in 2006. Also, they showed some mathematical results on their model. In the
model a carbonation front is given as a curve s(t) for time variable t > 0. In
order to improve their results we have simplified their model and obtained
theorems on existence and uniqueness of a solution to the model. Recently, we
have established the large time behavior of the carbonation fronts
mathematically. More precisely, we observe the existence of positive constants c
and C such that c ≤
s(t) ≤ C for
t ≥ 0. This tlaw
is usually used by engineers as the experimental law.
PRESENTATION
Goro Akagi (Kobe
Universtiy, Japan)
Nonlinear diffusion equations involving p(x)Laplacians
In this talk, we deal with nonlinear parabolic equations involving the
socalled p(x)Laplacians. We discuss wellposedness, largetime behaviors of
solutions and limiting problems as p(x) tends to infinity in the whole or a part
of domain. Our method of analysis is based on variational analysis and
subdifferential calculus. This talk is based on a joint work with Kei Matsuura (Waseda
University).
PRESENTATION
Jan Bouwe van den Berg (VU
Amsterdam)
Instabilities in singular solutions in the LandauLifshitzGilbert
problem
In this talk we use formal asymptotic arguments to
understand the stability properties of equivariant solutions to the LandauLifshitzGilbert
model for ferromagnets. We also analyze both the harmonic map heat flow and
Schrödinger map flow limit cases. All asymptotic results are verified by
detailed numerical experiments, as well as a robust topological argument. The
key result is that blowup solutions to these problems are codimension one and
hence both unstable and nongeneric.
PRESENTATION
Daan
Crommelin (CWI)
Stochastic subgrid scale modeling
In atmosphereocean science, the representation
(or parameterization) of subgrid scale processes in numerical models is a
notoriously difficult problem. Good representations (or lack thereof) of
processes such as convection, cloud physics and surface interactions directly
affect the quality and accuracy of forecasts and climate studies. In recent
years, researchers have turned to stochastic methods in order to improve these
parameterizations. I will discuss a stochastic, datadriven approach to the
problem, in which unresolved processes are represented by collections of
(datainferred) Markov processes that depend on resoved model variables. This
approach leads to hybrid stochasticdeterministic models consisting of
differential equations coupled to Markov chains.
Odo Diekmann (Utrecht University)
(joint
work with Mats Gyllenberg, Hans Metz and many others)
Delay Equations and Physiologically Structured Population Models
A delay equation is a
rule for extending a function of time towards the future, on the basis of the
known past. Renewal Equations prescribe the current value, while Delay
Differential Equations prescribe the derivative of the current value. With a
delay equation one can associate a dynamical system by translation along the
extended function.
I will illustrate by way
of examples how such equations arise in the description of the dynamics of
structured populations and sketch the available theory, while making a plea for
the development of numerical bifurcation tools.
PRESENTATION
Joep
Evers (TU Eindhoven)
(joint work Adrian Muntean)
Modelling multicomponent crowd dynamics via a twoscale, measuretheoretical
approach
We present a framework to describe the dynamics of crowds, in which the
behaviour of the crowd is considered from a twofold perspective: both
macroscopically (continuum) and microscopically (discrete). On both scales we
specify mass measures and their transport, and we unify the micro and macro
approaches in a single model.
We incorporate the ideas of mixture theory, which allows us to define several
constituents (read: subpopulations) of the large crowd, each having its own
partial velocity field. We thus have the possibility to examine the interactive
behaviour between subgroups that have distinct characteristics. We especially
aim at giving special properties to those pedestrians that are represented by
the microscopic (discrete) part in the model. In real life situations they would
play the role of leaders, terrorists, predators etc.
By identifying a suitable concept of entropy for the system, we derive an
entropy inequality. From this inequality restrictions on the proposed velocity
fields follow. Obeying these restrictions in the modelling phase, we make our
assumptions more feasible. Under certain conditions, the entropy inequality even
turns out to hold if we add anisotropy to the interactions. Anisotropy, in our
model, means that the vision (or: perception) of individuals depends on the
direction; people have a front and a back side.
Open questions concern the effect of leadership and anisotropy on the
largescale behaviour of the crowd. Do they influence the overall velocity
dramatically, for instance?
PRESENTATION
Yabin Fan (Eindhoven University of Technology)
Abstract
PRESENTATION
Tasnim
Fatima (TU Eindhoven)
(joint work with Adrian Muntean and Toyohiko Aiki)
Wellposedness of a nonlinear twoscale reactiondiffusion system modeling
concrete corrosion
We consider a twoscale reactiondiffusion system modeling concrete corrosion in
sewer pipes, which is defined on two different spatial scales. The system
consists of four PDEs one of which is a porous medi like equation, and an ODE.
The system is nonlinear, partially dissipative, and coupled via the solidwater
interface at the pore level and through the nonlinearity in the diffusion
coefficient of the moisture. This model is obtained by upscaling of the physiochemical
processes taking place in the microstructure of the pipes. We show existence,
uniqueness, L_^∞bounds and positivity of the weak solutions. To prove the
existence of weak solutions, we apply a twoscale Galerkin approach for a part
of the system combined with a Schauder fixedpoint argument for the moisture
equation.
PRESENTATION
Takesi
Fukao (Kyoto
University of Education, Japan)
Wellposedness for the variational inequality related to the NavierStokes
equations
In this talk, the existence problems for the
NavierStokes equations with constraint are considered in the 3dimensional
space. These problems are motivated by an initialboundary value problem for a
thermohydraulics model in which the absolute value of the velocity field
is constrained. The abstract theory of nonlinear evolution equations governed by
subdifferentials of timedependent convex functionals is useful. In their
mathematical treatment, the point of emphasis is to specify the class of
timedependence of convex functionals. First, wellposedness for the strong and
weak variational inequalities are considered. Second, the existence problem for
the NavierStokes equations with the temperature dependent constraint is
considered. This is a joint work with professor Nobuyuki Kenmochi, Bukkyo
University, Japan.
PRESENTATION
Junichi Harada (Waseda
University, Japan)
Singularity of blowup solutions to the heat equation with a nonlinear boundary
condition
We study the blowup profile of positive solutions the heat equation with a
nonlinear boundary condition for the Sobolev subcritical case. In particular, we
focus on spacial singularities of the blowup profile.
To apply arguments in HerreroVelazquez (9293), we establish some estimates for
a heat kernel of some linearized equation.
PRESENTATION
Charlotte K. Hemelrijk (University of
Groningen)
(joint work with Hanno Hildenbrandt)
Some causes of the
variable shape of flocks of birds
The variations
in shape in the aerial displays of huge flocks of starlings (Sturnus vulgaris)
above the sleeping site at dawn is amazing. Also other species of birds are
highly variable in the shape of their flocks, more so than fish schools; fish
schools are usually oblong. The causes of this variability, however, are hardly
known. We investigate these causes with the help of a model of the
selforganisation of a travelling group. In the present paper, we use a model,
called StarDisplay, whose flocking patterns resemble qualitatively and
quantitatively those of real birds, in particular starlings.
In it, individuals coordinate with nearby others through
attraction, alignment and avoidance (just as in models of fish schools). This is
supplemented with some specifics of starling behaviour, namely 1) their aerial
locomotion, 2) a low and constant number of interactionpartners and 3)
preferential movement above a ‘sleeping area’.
As to shape, we measure the relative proportions of the flock and the longest
dimension in respect of its direction of movement. We show that flock shape is
usually more variable when local differences in movement in the flock are larger.
This happens when a) flock size is larger, b) interacting partners are fewer, c)
the flock turnings are stronger, d) individuals roll into the turn. In contrast
to our expectations, when variability of speed in the flock is higher, its shape
and the positions of its members are more static. We explain this and indicate
the adaptive value of low variability of speed and spatial restriction of
interaction and develop testable hypotheses.
PRESENTATION
Tetsuya Ishiwata
(Shibaura Institute of Technology, Japan)
Behavior of polygonal curves by crystalline curvature flow
We consider 2 types of crystalline motion: One is areapreserving
crystalline motion and the other is crystalline curvature flow with a driving
force. These motion are simple models of interface motion inside/on a crystal:
The first model describes a deformation process of an interface of a negative
crystal and the second one is a model of a stepmotion on a crystal. In this
talk, we discuss a behavior of solution curves in the plane, especially, we
mainly consider a deformation of solution curves.
Akio
Ito (Kinki University, Japan)
Mathematical Model for Cardiomegaly of Spontaneously Hypertensive Rats
In this talk, we propose two mathematical models for cardiomegaly of a
spontaneously hypertensive rat (SHR), which is one of the model animals to
research the mechanism of various disease caused by hypertension. One model is a
system of ODEs established from the viewpoint of system biology and we will give
some numerical and experimental results. The other is a system of PDEs and ODEs,
which takes into consideration a space distribution of some functional proteins.
Finally, we give some idea to analyze our mathematical model by using the theory
of quasivariational inequality.
PRESENTATION
Risei Kano (Kinki
University, Japan)
The existence of solutions for tumor invasion models equipped with a diffusion
depending on some stress
We consider the tumor invasion model of Chaplain – Anderson type with the
effect of heat shock protein (HSP). This problem has the diffusion coefficient
that is depend on some variables. In this talk, we discuss the result of tumor
diffusion that is K_n=K_n(t,x,f) type.(time, place and unknown function ‘f’)
This is an extension of the condition that K_n=K_n(t,x) has been studied. In
addition, we introduce the results of computer simulations on models for the
effect of HSP.
PRESENTATION
Nobuyuki
Kenmochi (Bukkyo University,
Japan)
Revival Models of Human and Economic Activities in Disaster Areas
We learned a lot from serious disasters (earthquake,
tsunami, typhoon,....) which had attacked some places in Japan. In most cases
after disasters we face various problems, such as environment destroy for life
and economic collapse, etc. It is quite important to recover human and economic
activities in the disaster regions as soon as possible, by providing with
suitable supports for them. In general it takes a long time (10 or 20 years) to
recover the complete environment which is the basis of our life. Therefore,
actually one has to restart our life in incomplete circumstances. Moreover, at
the same time one has to start adequate reorganization of production systems in
order to recover the economical situation in the disaster regions.
We know many mathematical models dealing with the evolution of human activity
and the economic growth, independently each other. However, in disaster regions
the both aspects should be treated simultaneously on a correlative connection,
although the corresponding model is much more complicated than the above.
In this talk, we propose a simplified system of ordinary differential equations
(ODEs), which we call the revival full model of human and economic activities in
disaster regions. Our model consists of two systems (S) and (E) of ODEs. System
(S) describes the evolution of environmental parameter s of our life, and (E)
the economic growth parameter w in the disaster regions and nondisaster regions.
One of crucial points in our modeling is how to express mathematically the
correlative relationship between s and w as well as some sufficient condition
for the selfreliant growth of w, namely the revival of economy. The full model
is discussed in four periods: in the first period the main support is given by
the public funds, in the second period it is given by both of the public and
private (local) funds and in the third period it is given only by the private (local)
funds. In the final period we expect to reach the economically stable situation,
that is, the economic growth is achieved without any support, but the
environment recovery is still in process of development.
PRESENTATION
Kundan Kumar (Eindhoven
University of Technology)
Abstract
Kota Kumazaki
(Nagoya University, Japan)
Well posedness of a mathematical model of carbon dioxide transport in concrete
carbonation process
Concrete carbonation is a phenomenon that alkalinity by calcium hydroxide in
cementitious material changes into acidity because of carbon dioxide in air.
Concrete carbonation has been studied as a free boundary problem in one
dimensional case so far. Recently, in three dimension case we propose a
mathematical model of moisture transport in this process, and proved the
existence of a time global solution of this model. As the second step for
analyzing of the dynamics of concrete carbonation in three dimension, we focus
on carbon dioxide transport. In this talk we propose a initial boundary value
problem for a parabolic type equation as a mathematical model of carbon dioxide
transport in this process, and give the existence results of a time global
solution of this problem.
PRESENTATION
Roeland Merks (CWI, Amsterdam)
Cellbased modeling of
angiogenic blood vessel sprouting: cellECM interaction and tipcell selection
Angiogenesis, the growth of new blood vessels from existing ones, is a topic of
intensive experimental investigation so its phenomenology, the participating
cell types, and the molecular signals contributing to it have been well
characterized. Yet it is poorly understood how these biological components fit
together dynamically to drive the outgrowth of blood vessels. Cellbased
simulation models of blood vessel growth describe the behavior of cells and the
chemicals they produce. They then predict the collective behavior resulting from
cellcell interactions. Thus they help analyze how cells assemble into blood
vessels, and reveal how cell behavior depends on the microenvironment the cells
produce collectively.
Our simulation models, based on a Cellular Potts model combined with reactiondiffusion
equations, have shown that the elongated shape of cells is key to correct
spatiotemporal in silico replication of vascular network growth. We also
identified a new stochastic mechanism for blood vessel sprouting. Here I will
briefly discuss new insights into the role of cell shape and stochastic motility
during vascular branching. Then I will present recent results on the role of tip
cells, suggesting that tip cellstalk cell interactions accelerate angiogenic
sprouting. I will also discuss our recent cellbased modeling studies of cellextracellular
matrix interactions during angiogenesis.
PRESENTATION
Yusuke Murase (Meijo University, Japan)
Nonlinear evolution equations for mathematical modeling for brewing process of
Japanese Sake
In this talk, we introduce our mathematical modeling
for brewing process of Japanese Sake, and discuss solvability of nonlinear
evolution equations which is corresponding to parabolic quasivariational
inequalities. Our evolution equations are generated by subdifferentials and some
perturbations. In addition, we explain the relationship between the evolution
equations and mathematical modeling.
PRESENTATION
Yuko Nagase (University of Crete)
On the existence of solution for a CahnHilliard/ AllenCahn
equation
In
this talk, we consider a CahnHilliard/AllenCahn equation, which was derived in
KaraliKatsoulakis. This mean field partial differential equation contains
qualitatively microscopic information on particleparticle interactions and
multiple particle dynamics. In a suitable scaling, the singular limit of this
equation is mean curvature flow, like AllenCahn equation, but with a different
mobility. As a mathematical analysis, we improve the existence of solution for a
standard doublewell potential in dimension 1 to 4 in view of the free energy.
We also mention about the stochastic version of this equation.
Robert Nolet (VU Amsterdam)
Existence of
solutions for the diffusive VSC model
The diffusive
VSC model describes the growth of fungal hyphae. It assumes that building
materials for the cell wall are produced inside the cell and diffuse outwards,
where they are assimilated causing the cell wall to expand orthogonally. This
yields a geometric evolution equation for the surface of the cell. In this talk
we will show how to prove the existence of travelling solutions, similar to
those observed experimentally.
Takeshi Ohtsuka (Gunma University, Japan)
Stability of bunched steps in spiral crystal growth
Burton, Cabrera and Frank proposed the theory of the evolution of
monomolecular spiral steps on the crystal surface in 1951. Kobayashi or Karma
and Plapp proposed an AllenCahn type equation, and Smereka or the speaker
proposed a level set formulation for the evolution of spiral curves,
respectively. On the other hand, one can find the spiral patterns by multiple
molecular height of steps on crystal surface in physical experiences. Thus, the
stability of bunched steps is concerned.
However, instability of bunched steps by AllenCahn type equation are derived
by Ogiwara and Nakamura.
In this talk we consider evolution of bunched spiral curves with the level set
formulation by the speaker. Our model is derived from asymptotic expansion of
the AllenCahn type equation.
However, we prove the stability of bunched steps in the level set equation.
PRESENTATION
Mitsuharu Ôtani
(Waseda Universirty, Japan)
On BrinkmanForchheimer equations of flow in doublediffusive convection
Abstract
Mark Peletier
(TU/e)
Size doesn't matter, it's the way you stack it: upscaling dislocations
Permanent deformation of metals results from the collective motion of a large
number of dislocations. These dislocations are defects in the atomic lattice,
and their motion causes the atomic layers to slide over each other. Many of
these atomicscale sliding events may combine to produce a macroscopic change of
geometry that we observe as permanent deformation.
Although good models are available both at the level of the atomic lattice and
at the level of continuum mechanics, there currently is no method, formal or
rigorous, that allows us to take a limit and connect the different scales in a
convincing way. This is a major obstacle for the design and engineering of
highperformance steels.
In this talk I describe recent progress in this area, together with Lucia
Scardia, Marc Geers, and Ron Peerlings. I will show how a simplified setup
produces new insight into this difficult connection, and provides a hint as to
how we should think about the more general case.
PRESENTATION
Sorin Pop (TU/e)
The mathematics of salt: from pore to core
In
this presentation we focus on a mathematical model for dissolution and
precipitation in porous media. The model fits into a generic framework
applicable in various contexts, including bioremediation, drug release, battery
modelling, weathering of stones or concrete carbonation. Compared to similar
models for reactive flows, the particularity encountered here is in the modeling
of the dissolution. This involves a multivalued rate and can explain the
occurrence of dissolution fronts.
After addressing some modeling details, we present results concerning the
existence and uniqueness of a weak solution at the pore scale. Next, we employ
upscaling techniques to derive the corresponding model at the core (laboratory)
scale, for which
existence and uniqueness results are provided.
This is a joint work with C.J. van Duijn, K. Kumar (both Eindhoven), A. Mikelic
(Lyon), T.L. van Noorden, M. NeussRadu (both Erlangen), and F.A. Radu (Bergen)
PRESENTATION
Georg
Prokert (TU
Eindhoven)
(Joint work
with M. Günther, Universität Leipzig)
Traveling Waves in a HeleShaw Type Moving Boundary Problem
We discuss a 2D
movingboundary problem for the Laplacian with Robin boundary conditions in an
exterior domain. It arises as model for HeleShaw ﬂow of a bubble with kinetic
undercooling regularization and is also discussed in the context of models for
electrical streamer discharges.
The
corresponding evolution equation is given by a degenerate, nonlinear transport
problem with nonlocal lowerorder dependence. We identify the local structure of
the set of travelingwave solutions in the vicinity of trivial (circular) ones.
We ﬁnd that there is a unique nontrivial traveling wave for each velocity near
the trivial one. Therefore, the trivial solutions are unstable in a comoving
frame.
The degeneracy
of our problem is reﬂected in a loss of regularity in the estimates for the
linearization. Moreover, there is an upper bound for the regularity of its
solutions.
PRESENTATION
Jens
Rademacher (CWI, Amsterdam)
Coherent
structures and patterns in Magnetization
We
consider spatiotemporal pattern formation in spatially onedimensional LandauLifschitzGilbert
equations modelling the evolution of magnetization in materials. We prove
existence of a rich class of patterns composed of wavetrains and/or homogeneous
states, and also discuss stability. This is joint work with Christof Melcher (RWTH
Aachen).
Frank
Redig (TU Delft)
(joint work with Feijia Wang (Leiden))
Large deviations for
Markov processes conditioned on the future
Motivated by socalled
GibbsnonGibbs transitions, we study diffusion processes with small variance
starting from an initial measure that satisfies the large deviation principle,
and conditioned to end at a fixed point in the future. We show that for large
times, the optimal trajectories can be nonunique. The same behavior is shown
for birth and death processes close to their deterministic limit.
PRESENTATION
Okihiro
Sawada
(Gifu
University, Japan)
On the norminflation solutions to the NavierStokes equations in the critical
space
The illposedness
of the incompressible 3D NavierStokes equations in the critical Besov space is
concerned. A lack of the equicontinuity was shown by BourgainPavlovic, using
the norminflation argument of mild solutions (solutions of the integral
equation via the heat semigroup). In this talk, the termwise estimates for the
sequence of successive approximation of a mild solution are derived. This leads
us to a rigorous proof of the illposedness theory. Moreover, from the same
ideas of BourgainPavlovic, the necessity of taking a `good' subsequence of the
successive approximation is also proved. Indeed, there exists a `bad' subsequece
who diverges.
PRESENTATION
Ken Shirakawa (Chiba University, Japan)
Energydissipative solution to onedimensional phase field model of grain
boundary
This study is a joint work with Dr. Hiroshi Watanabe, Salesian Polytechnic,
Japan.
In this talk, a onedimensional system of two parabolic type equations is
considered. This system is based on a phase field model of grain boundary,
proposed by KobayashiWarrenCarter [Physica D, 140 (2000), 141150], and it is
derived as a gradient flow of a governing energy, called freeenergy.
The focus in this talk is on a special kind of solution, named as
"energydissipative solution", which realizes the dissipation of the freeenergy
in time. Consequently, the existence of energydissipative solution and some
related topics will be presented as the main results of this talk.
PRESENTATION
Igor
Stojković
(Delft Institute of Applied Mathematics)
Maximal Monotone Operators in Wasserstein
Spaces of Probability Measures
Abstract
PRESENTATION
Takashi
Suzuki
(Osaka University, Japan)
Globalintime behavior of a GiererMeinhardt system
GiererMeinhardt system describes morphogenesis of hydra in the context of
Turing patterns. There is a parameter region where the ODE part takes periodic
orbits. If two diffusion coefficients are comparable in this parameter region,
then any solution exists globalintime and is absorbed into one of the ODE
orbit. An underlying variational structure is revealed applicable to other
biological models; joint work with G. Karali and Y. Yamada.
PRESENTATION
Souhei
Tasaki (Osaka
University, Japan)
(joint work with Irena Pawlow and Takashi Suzuki)
Stationary solutions to a straingradient type thermoviscoelastic system
We study a
straingradient type thermoviscoelastic system. We focus on the stationary
states and their dynamical stability. The adiabatic stationary state is
formulated as a nonlinear eigenvalue problem with nonlocal terms associated
with the total energy conservation. We reveal a unified structure, called
semidualities, of the thermoviscoelastic system of viscositycapillarity type
with temperaturedependent viscous and elastic moduli. Based on the semidual
structure we construct a series of general results concerning the stationary
states and their stability. The application of these results together with the
bifurcation theory allows to analyze the total set of the stationary solutions
in more detail.
PRESENTATION
Tohru Wakasa (Meiji University, Japan)
Mathematical analysis for a simplified tumor growth model with
contactinhibition
In the last two decades several mathematical models on tumor growth has been
discussed by many researchers. For a competying process between the normal cells
and the abnormal cells, Chaplain, Graziano and Presiozi have proposed a
macroscopic 5 component PDE model of reactiondiffusion type. From a viewpoint
of contactinhibition of cells, which is commonly observed for colony formation
in vitro (and vivo), a simplified system for two cell populations has been
introduced and analyzed by Bertsch, DalPasso and Mimura. This
contactinhibition model, shows us a segregated property: if the initial
distribution for normal and abnormal cells are segregated from each other, the
solution keeps segregated after the contact.
We are interested in a qualitative behavior of the solutions to the
contactinhibition model including segregating/overlapping properties. In this
talk we consider the onedimensional model, and based on numerical evidence for
the initial value problem, mathematical results on a free boundary formulation
and traveling wave solutions are given.
This talk is based on the joint work with Professors Michiel Bertsch and
Masayasu Mimura.
PRESENTATION
Hiroshi Watanabe (Salesian
Polytechnic, Japan)
Solvability of boundary value problems for strongly degenerate parabolic
equations with discontinuous coefficients
Strongly degenerate parabolic equations are
regarded as a linear combination of the timedependent conservation laws (quasilinear
hyperbolic equations) and the porous medium type equations (nonlinear degenerate
parabolic equations). Thus, this equations has both properties of hyperbolic
equation and those of parabolic equations and describes various nonlinear
convective diffusion phenomena such as filtlation problems, Stefan problems and
so on.
In this talk we consider that strongly degenerate parabolic equation has
discontinuous coefficients. In particular, we forcus our attention on boundary
value problems for this type of equations. In fact, we show the unique existence
of weak solutions for the Neumann problem and the zeroflux boundary value
problem. We explain construction of the weak solutions using compensated
compactness method and Hmeasure.
PRESENTATION
Martijn Zaal (VU Amsterdam)
Gradient Flow Model for Osmotic Cell Swelling
A basic model
for cell swelling by osmosis is constructed, resulting in a free boundary
problem. For radially symmetric initial conditions, this model can be formulated
as a gradient flow on a metric by choosing a suitable pair of functional and
metric. This particular choice does not require the osmotic force to be included
in the formulation explicitly. It appears that this result can be generalized to
nonsymmetric initial conditions.
PRESENTATION
Practical information
Conference Location
The workshop location is EURANDOM, Den Dolech 2, 5612 AZ Eindhoven,
Laplace Building, 1st floor, LG 1.105.
EURANDOM is located on the campus of
Eindhoven
University of Technology, in the
'Laplacegebouw' building' (LG on the map). The university is located at
10 minutes walking distance from Eindhoven railway station (take the exit
north side and walk towards the tall building on the right with the sign
TU/e).
For all information on how to come to Eindhoven, please check
http://www.eurandom.tue.nl/contact.htm
Contact
For more information please contact
Mrs. Patty Koorn,
Workshop officer of EURANDOM
Sponsored by:
Last updated
281111,
by
PK
