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July 2005 Intermediate dynamics of internal layers for a nonlocal reaction-diffusion equation
Koji Okada
Hiroshima Math. J. 35(2): 263-308 (July 2005). DOI: 10.32917/hmj/1150998275


A singular perturbation problem for a reaction-di¤usion equation with a nonlocal term is treated. We derive an interface equation which describes the dynamics of internal layers in the intermediate time scale, i.e., in the time scale after the layers are generated and before the interfaces are governed by the volume-preserving mean curvature flow. The unique existence of solutions for the interface equation is demonstrated. A continuum of equilibria for the interface equation are identified and the stability of the equilibria is established. We rigorously prove that layer solutions of the nonlocal reaction-di¤usion equation converge to solutions of the interface equation on a finite time interval as the singular perturbation parameter tends to zero.


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Koji Okada. "Intermediate dynamics of internal layers for a nonlocal reaction-diffusion equation." Hiroshima Math. J. 35 (2) 263 - 308, July 2005.


Published: July 2005
First available in Project Euclid: 22 June 2006

zbMATH: 1097.35017
MathSciNet: MR2176054
Digital Object Identifier: 10.32917/hmj/1150998275

Primary: 35K57
Secondary: 35B25

Rights: Copyright © 2005 Hiroshima University, Mathematics Program


Vol.35 • No. 2 • July 2005
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