Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 99, pp. 1-13.

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

Authors: Janete Crema (Inst. de Ciencias Mat., Carlos, S. P., Brasil)
         Arnaldo Simal do Nascimento (Univ. Federal de Sao Carlos, Brasil)
 
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.