| speaker | type | title |
| Philippe LAURENCOT | invited speaker | A thin fi lm approximation of the Muskat problem |
| abstract: Existence of self-similar solutions to a thin film approximation of the Muskat problem is investigated. This model describes the space-time evolution of the heights of two layers of non-miscible fluids with different viscosity and density and the dynamics is given by a second-order parabolic system featuring a diffusion matrix which is full and degenerate. After recalling the existence of solutions which relies on a gradient flow structure of the system, a classifi cation of self-similar solutions is given and their role in the large time behaviour is studied. Joint works with Bogdan Matioc (Hannover). |
| Beomjun Choi | participating speaker | MACROSCOPIC SCALE CONVERGENCE OF A MICROSCOPIC KINETIC MODEL TO STARVATION DRIVEN DIFFUSION |
| abstract: The purpose of this work is to derive a starvation driven diffusion operator from a diffusion limit of a microscopic scale kinetic model for a species with two phenotypes having different motility constants. |
| Bradley | participating speaker | KmKKgIvDJwVMMgL |
| abstract: lMlbzLkshNIjN |
| Chang-Wook Yoon | participating speaker | Cell aggregation without gradient sensing |
| abstract: We consider a Keller-Segel model describing cell aggregation phenomena. The model is formulated under the assumption that microscopic scale bacteria does not sense the macroscopic scale concentration gradient of chemical. We focus on the global existence of solutions and the steady states having aggregation structures. |
| Choi, Sun-Ho | participating speaker | A chemotaxis model with metric of food |
| abstract: The meaningful migration distance of biological organisms is not necessarily given by the Euclidean metric. A distance system that counts the amount of resources such as food could be more meaningful in many cases. It is assumed in this paper that the migration distance of biological organisms is measured by the amount of food between two points. A new chemotaxis model is introduced as an application of this metric of food. It is shown that, if the length of the random walk is given by such a metric, the well-known traveling wave phenomena of the chemotaxis theory can be obtained without the typical assumption that microscopic scale bacteria may sense the macroscopic scale gradient chemical concentration. The uniqueness and existence of traveling solutions of pulse and front types are proved. |
| Danielle Hilhorst | invited speaker | Mathematical analysis of a PDE model describing chemotactic E. coli colonies |
| abstract: We consider an initial-boundary value problem describing the formation of colony patterns of bacteria Escherichia coli. This model consists of reaction-diffusion equations coupled with the Keller-Segel system from the chemotaxis theory in a bounded domain, supplemented with zero-flux boundary conditions and with nonnegative initial data. We answer questions about the global in time existence of solutions as well as on their large time behavior. Moreover, we show that the solutions of a related model may blow up in finite time. This is joint work with R. Celinski, G. Karch and M. Mimura. |
| Dohyun Kwon | participating speaker | Starvation Driven Diffusion in a Prey-Predator Model |
| abstract: In the paper we study the effect of starvation driven diffusion when it is applied to prey or predator species. If this smarter migration strategy is applied to the prey species, the prey species has better chance to prosper and the predator species has less chance to survive. However, if it is applied to the predator species, both species are beneficial. Indeed, the regime that the prey species is beneficial to predator species. Of course, the survival of prey is beneficial to predator. |
| Fang Li | participating speaker | NONLOCAL EFFECTS IN SOME MATHEMATICAL MODELS FROM BIOLOGY |
| abstract: In this talk, we discuss how nonlocal terms qualitatively or quantitatively affect the properties of solutions using ecological models, genetic model and Gierer-Meinhardt model as examples. In general, we compare local models and their nonlocal counterpart. For different models, we study nonlocal effects from different aspects and obtain some interesting results. |
| Hideki Murakawa | invited speaker | A linear finite volume method for nonlinear cross-diffusion systems |
| abstract: In this talk, we propose and analyze a linear finite volume scheme for general nonlinear cross-diffusion systems. The scheme consists of discretization of linear elliptic equations and pointwise explicit algebraic corrections at each time step. Therefore, the scheme can be implemented very easily. The proposed finite volume method is an unconditionally stable, convergent and conservative scheme. We establish error estimates for the method. |
| Hirofumi Izuhara | participating speaker | Pattern formation in chemotaxis-growth systems |
| abstract: |
| Jaewook Ahn | participating speaker | Time Decay of the solutions of the Angiogenesis type system |
| abstract: We consider a simple model arising in modeling angiogenesis. That is, the development of capillary blood vessels due to and exogeneous chemo attractive signal. We show the gain of L^{infty} integrability for sufficiently small initial data when the spatial dimensions are more than 2. |
| Jaywan Chung | participating speaker | Bistable nonlinearity having a discontinuity |
| abstract: The traveling wave phenomenon of a reaction diffusion equation is well understood understood then the reaction is given by a bistable non-linearity. In this talk we consider a case when such a non-linearity has a discontinuity near the zero population. Using such a non-linearity, we show the behavior of corresponding traveling wave as a limit of the continuously perturbed problem. The convergence and the existence of front of the support are obtained. |
| Kyungkeun Kang | participating speaker | On regularity for the Chemotaxis-Navier-Stokes Equations |
| abstract: |
| Laurent Desvillettes | invited speaker | Some recent results for cross diffusion equations |
| abstract: In a common work with Thomas Lepoutre, Ayman Moussa and Ariane Trescases, we study cross diffusion systems arising from population dynamics, and extending the classical model of Shigesada-Teramoto-Kawasaki. We put in evidence an entropy structure for the cross diffusion part of those systems, which enables to prove existence of weak solutions for a large class of coefficients, and sheds new light on the results of L. Chen and A. Juengel obtained in the mid-2000s. |
| LOGAK Elisabeth | invited speaker | A nonlocal system modelling the spread of epidemics on networks |
| abstract: We consider a nonlinear SIS-type integro-differential system which is the continuous version of a discrete model for the propagation of epidemics on networks. Under the assumption of limited or nonlimited transmission, we prove the existence of a global unique solution. We also prove the existence of an endemic equilibrium in a large class of networks under some threshold condition. We investigate linear stability and obtain nonlinear stability results in the case of limited transmission, that can be compared to the ones previously known for the discrete model. |
| Lorenzo CONTENTO | participating speaker | Two-dimensional traveling waves in a three-species competition-diffusion system |
| abstract: Three-species competition-diffusion systems may admit two different planarly stable traveling wave solutions. The study of the interaction of these waves in one dimension has been shown to offer insight about whether or not coexistence occurs in two-dimensional domains. However, when planar fronts collide at a certain angle, phenomena which are not immediately reducible to the one-dimensional case can be observed. Such interactions produce different types of moving patterns which seem to tend to truly two-dimensional traveling waves, such as wedge-shaped waves. |
| Masaharu Taniguchi | invited speaker | Multidimensional traveling fronts in reaction-diffusion equations |
| abstract: In this talk I first survey recent studies on traveling fronts of reaction-diffusion equations in multidimensional spaces. Next I explain my recent work on traveling fronts in unbalanced Allen--Cahn equations and cooperation-diffusion systems. Let an integer N be greater than 2. Let (N-2)-dimensional smooth surfaces be given as boundaries of strictly convex compact sets in the (N-1)-dimensional space. I prove that there exists an N-dimensional traveling front associated with a given surface and show its stability. |
| Masayasu Mimura | invited speaker | Colonial Patterns in Chemotactic E.coli |
| abstract: |
| Matthieu ALFARO | invited speaker | Slowing Allee effect vs accelerating heavy tails in population dynamics models |
| abstract: We focus on the spreading properties of solutions to some monostable reaction diffusion equations which serve as population dynamics models. In KPP situations, it is known that heavy tails lead to accelerating solutions. We introduce a weak Allee effect which tends to slow down the process. We discuss new developements on the balance between these two opposite effects. |
| Michel Chipot | invited speaker | On some nonlocal problems |
| abstract: We will present some recent results on asymptotic behaviour for some nonlocal parabolic problems. |
| Ohsang Kwon | participating speaker | The e ffects of starvation driven diff usion on the dynamics of populations |
| abstract: The starvation driven diffusion is an example of dispersal strategies of biological organisms that increases the motility when food is not enough to support the population. In this talk, we will discuss properties of the single species model and 2 by 2 competition model with starvation driven diffusion, including the global asymptotic stability and the acquisition of the ideal free distribution. We show that such a dispersal strategy has fitness property and that the evolutional selection favors fitness but not simply slowness. This is the joint work with Y.-J. Kim and F. Li. |
| Shin-Ichiro Ei | invited speaker | Dynamics of solutions for chemotaxis-growth systems |
| abstract: |
| Yangjin Kim | invited speaker | The role of chemotaxis and diffusion processes in tumor growth models |
| abstract: Chemotaxis and diffusion processes play an important roles in regulation of cancer progression. For example, chemotaxis is an important requirement for cancer metastasis when the tumor cells get out of the huge tumor mass in response to various biological factors such as chemotactic attractants. We introduce several mathematical models that take into accounts these important processes, and predictions out of the mathematical models. |
| Yaping Wu | invited speaker | Traveling Waves and Steady States for S-K-T Competition Model with Cross-Diffusion |
| abstract: In this talk we shall be focused on a quasilinear reaction diffusion system with cross diffusion, which was first proposed by Shigesada, Kawasaki and Teramoto in 1979 for investigating the spatial segregation of two competing species under inter- and intra-species population pressures. I shall talk about some recent research progress on the existence and stability of nontrivial steady states and travelling waves for the S-K-T competition model with cross diffusion, which may correspond to some new pattern formation and wave phenomena induced by cross diffusion. |
| Yong Jung Kim | invited speaker | Diffusion with non-constant steady states |
| abstract: Many of biological species increase their dispersal rate if starvation starts. To model such a behavior we need to understand how organisms measure starvation and response to it. In this paper we compare three different ways of measuring starvation by applying them to starvation driven diffusion. The evolutional selection and coexistence of such starvation measures are studied within the context of Lotka-Volterra type competition model of two species. We will see that, if species have different starvation measures and different motility functions, both the coexistence and selection are possible. It is spatial heterogeneity, but not nonlinearity, that gives nonconstant steady state driven by diffusion. The starvation driven diffusion is of such a type. |