Seminar on Qualitative Theory of Differential Equations - Toru Kan (8.2.2018)
Thursday 8.2.2018 at 14:00 hod., Lecture room M/223
By: Pavol Quittner
Toru Kan (Tokyo Institute of Technology):
Stationary solutions of bistable reaction-diffusion equations on some thin tubular domain
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.