### Seminar 8.2.2018: Toru Kan

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**Sun Feb 04, 2018 10:34 am**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.

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.