[00554] Pattern dynamics appearing in mathematical biology
Session Time & Room : 4E (Aug.24, 17:40-19:20) @G406
Type : Proposal of Minisymposium
Abstract : Biological phenomenon have promoted the mathematical studies of pattern dynamics, such as Turing's pattern formation and traveling wave. We will introduce some of the recent progress around this topic which offer new viewpoints. We hope this is going to be the starting point to discuss the future perspective.
00554 (1/1) : 4E @G406 [Chair: Toshiyuki Ogawa, Hirokazu Ninomiya]
[01234] Turing's instability by equal diffusion
Format : Talk at Waseda University
Author(s) :
Hirokazu Ninomiya (Meiji University)
Abstract : In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium of some kinetic system is destabilized by diffusion. In the case of two-component reaction-diffusion systems, however, the diffusion coefficients should be different. This talk presents an example of a two-component kinetic system with a asymptotically stable equilibrium, while the corresponding reaction-diffusion system has a family of unstable stationary solutions that is arbitrarily close to the homogeneous stationary solution.
[01275] Reaction-diffusion fronts in funnel-shaped domains
Format : Talk at Waseda University
Author(s) :
Mingmin Zhang (Universite Toulouse III - Paul Sabatier)
Abstract : We study large-time dynamics of entire solutions to bistable equations in funnel-shaped domains emanating from a planar front in the straight part and moving into the conical part. We prove a dichotomy between blocking and spreading, and show that any spreading solution is a transition front whose level sets have roughly expanding spherical shapes at large times. We provide sufficient conditions on geometry of the domains, under which the solution is blocked or spreads completely.
[01442] Traveling wave solution in a macroscopic traffic model
Format : Talk at Waseda University
Author(s) :
Kota Ikeda (Meiji UniversityMeiji University)
Abstract : Various subjects in traffic dynamics have long posed a challenge. Theoretical approaches have revealed the localized and extended forms of congestion with the propagation velocity of stop-and-go waves in models. In 2001, Lee et al. derived a macroscopic traffic model from an OV model and numerically showed that a traveling pulse appears under a relatively high density of cars. We prove the existence of such a traveling pulse rigorously via a phase plane method.
[03160] Bistable pulsating fronts in showling oscillating environments
Format : Talk at Waseda University
Author(s) :
Weiwei Ding (South China Normal University)
Abstract : In this talk, I will present some progress on reaction-diffusion fronts in spatially periodic bistable media. The results include: existence of pulsating fronts with large periods, existence of and an explicit formula for the limit of front speeds as the spatial period goes to infinity, convergence of pulsating front profiles to a family of front profiles associated with spatially homogeneous equations. This talk is based on joint work with Francois Hamel and Xing Liang.
