## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 38, Number 2 (2008), 263-313.

### Dynamical approximation of internal transition layers in a bistable nonlocal reaction-diffusion equation via the averaged mean curvature flow

#### Abstract

A singular perturbation problem for a scalar bistable nonlocal reaction-diffusion equation is treated. It is rigorously proved that the layer solutions of this nonlocal reaction-diffusion equation converge to solutions of the averaged mean curvature flow on a finite time interval as the singular perturbation parameter tends to zero.

#### Article information

**Source**

Hiroshima Math. J., Volume 38, Number 2 (2008), 263-313.

**Dates**

First available in Project Euclid: 5 September 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1220619461

**Digital Object Identifier**

doi:10.32917/hmj/1220619461

**Mathematical Reviews number (MathSciNet)**

MR2437575

**Zentralblatt MATH identifier**

1156.35008

**Subjects**

Primary: 35B25: Singular perturbations 35K57: Reaction-diffusion equations

**Keywords**

Singular perturbation bistable nonlocal reaction-diffusion equation internal transition layer interface the averaged mean curvature flow

#### Citation

Okada, Koji. Dynamical approximation of internal transition layers in a bistable nonlocal reaction-diffusion equation via the averaged mean curvature flow. Hiroshima Math. J. 38 (2008), no. 2, 263--313. doi:10.32917/hmj/1220619461. https://projecteuclid.org/euclid.hmj/1220619461