[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Toru Kan (Tokyo Institute of Technology)
Abstract: Reaction-diffusion equations are mathematical models describing the time evolution of spatial patterns in physical phenomena. The existence and stability of nonconstant stationary solutions are therefore one of main interests in the study of reaction-diffusion equations. For one-component reaction-diffusion equations with the Neumann boundary condition on a bounded domain, a stable nonconstant stationary solution can exist if the domain is dumbbell-shaped and the reaction term is bistable. Such a stable solution exists only if the reaction rate is not small, hence it appears through a bifurcation if the reaction rate is regarded as a bifurcation parameter. In this talk, in the case that the domain is close to a line segment, we find how it appears in the bifurcation diagram.