Janete Crema, Arnaldo Simal do Nascimento
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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Arnaldo Simal do Nascimento
Departamento de Matematica
Universidade Federal de Sao Carlos
S. Carlos, S.P., Brasil