Destabilization threshold curves for diffusion systems with equal diffusivity under non-diagonal flux boundary conditions

Kunimochi  Sakamoto

doi:10.3934/dcdsb.2016.21.641

Article Contents

2016, Volume 21, Issue 2: 641-654. Doi: 10.3934/dcdsb.2016.21.641

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Destabilization threshold curves for diffusion systems with equal diffusivity under non-diagonal flux boundary conditions

Kunimochi Sakamoto^1,

1.
Graduate School of Science, Department of Mathematical and Life Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526

Received: November 30, 2014

Revised: August 31, 2015

Published: February 2016

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Abstract

This article deals with destabilizations of Turing type for diffusive systems with equal diffusivity under non-diagonal flux boundary conditions. Stability-instability threshold curves in the complex plane are described as the graph of a piecewise analytic function for simple $m$-dimensional domains $(m\geq 1)$. Also analyzed are effects caused by imposing homogeneous boundary conditions of Dirichlet or Neumann type on appropriate portions of the domain boundary.

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Mathematics Subject Classification: Primary: 35K40, 35J25; Secondary: 35J15.

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