PDE Seminar (2017/5/12): Bifurcation in scalar bistable reaction-diffusion equations on a thin dumbbell-shaped domain

2017-5-12 16:30 - 2017-5-12 17:30
Faculty of Science Building #3, Room 309
Toru Kan (Tokyo Institute of Technology)
We consider a bifurcation problem for scalar bistable reaction-diffusion equations with the Neumann boundary condition. We particularly focus on the case that the domain is dumbbell-shaped and close to a line segment. Then the equation can be approximated by some one-dimensional limiting equation. After introducing what the limiting equation should be, we show that the limiting equation indeed approximates the original equation. Finally we discuss the solution structure of the limiting equation.