Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 8.2.2018 at 14:00 Lecture room M-223

Toru Kan (Tokyo Institute of Technology):

Stationary solutions of bistable reaction-diffusion equations on some thin tubular domain

Abstract:

On a thin tubular domain, we consider a scalar bistable reaction-diffusion equation

with the Neumann boundary condition. The domain is given as a tubular neighborhood

of a line segment such that the middle part is much thinner than the other part.

Since the domain is close to a line segment, the equation is expected to be approximated

by some one-dimensional limiting equation. After formally deriving the appropriate limiting equation,

we show that it indeed approximates the original equation.

Then we consider the solution structure of the limiting equation.