This article is cited in 1 paper

Properties of spatial structures for reaction–nonlinear diffusion equations subject to Dirichlet conditions

V. N. Razzhevaikin

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia

Abstract: For reaction–nonlinear diffusion equations subject to Dirichlet homogeneous boundary value conditions, the properties of alternation of stable and unstable time-independent unimodal solutions are investigated. For the case of constant diffusion, formulas for the functions determining the type of stability are given and the results of their application to the case of quadratic nonlinearity in the source term are presented.

Key words: nonlinear reaction–diffusion equation, spatial structures, Dirichlet boundary conditions, stability of time-independent unimodal solutions.

UDC: 519.633

Received: 01.03.2011

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:10, 1729–1737

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