Hiroshima Mathematical Journal

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

Koji Okada

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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


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