The singular limit problem in a phase separation model with different diffusion rates $^*$

Kelei Wang

doi:10.3934/dcds.2015.35.483

Article Contents

2015, Volume 35, Issue 1: 483-512. Doi: 10.3934/dcds.2015.35.483

This issue Previous Article On the quasi-periodic solutions of generalized Kaup systems Next Article Decay rates of the compressible Navier-Stokes-Korteweg equations with potential forces

The singular limit problem in a phase separation model with different diffusion rates $^*$

Kelei Wang^1,

1.
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071

Received: August 2013

Revised: June 2014

Published online: August 2014

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Abstract

In this paper we study the singularly perturbed parabolic system of competing species. This problem exhibit a ``phase separation" phenomena when the interaction between different species is very strong. We are concerned with the case where different species may have different diffusion rates. We identify its singular limit with the heat flow (i.e. gradient flow) of harmonic maps into a metric space with non-positive curvature, by establishing the system of differential inequalities satisfied by this heat flow and uniqueness of the solution to the corresponding initial-boundary value problem.

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Mathematics Subject Classification: Primary: 35B25, 35R35; Secondary: 49N60.

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