Electron. J. Diff. Eqns., Vol. 1997(1997), No. 22, pp 1-17.
Arnaldo Simal do Nascimento
We use -convergence to prove existence of stable multiple-layer stationary solutions (stable patterns) to the reaction-diffusion equation.
Given nested simple closed curves in , we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.
Submitted May 13, 1997. Published December 1, 1997.
Math Subject Classification: 35K20, 35K57, 35B25.
Key Words: Diffusion equation, Gamma-convergence, transition layers, stable equilibria.
Show me the PDF file (224 KB), TEX file, and other files for this article.