Electron. J. Diff. Eqns., Vol. 2004(2004), No. 99, pp. 1-13.

On the role of the equal-area condition in internal layer stationary solutions to a class of reaction-diffusion systems

Janete Crema, Arnaldo Simal do Nascimento

Abstract:
We present necessary conditions for the formation of internal transition layers in stationary solutions to some singularly perturbed reaction-diffusion systems. In particular we prove that the well-known equal-area condition which is always assumed in a typical set of sufficient conditions for existence of such solutions is actually a necessary hypothesis. Examples of existence and nonexistence of these solutions are given.

Submitted January 13, 2003. Published August 12, 2004.
Math Subject Classifications: 35B25, 35B35, 35K57, 35R35.
Key Words: Reaction-diffusion system; internal transition layer; equal-area condition.

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Janete Crema
Instituto de Ciencias Matematicas e de Computacao-USP,
S. Carlos, S. P., Brasil
email: janete@icmc.sc.usp.br

Arnaldo Simal do Nascimento
Departamento de Matematica
Universidade Federal de Sao Carlos
S. Carlos, S.P., Brasil
email: arnaldon@dm.ufscar.br

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