Electron. J. Diff. Eqns.,
Vol. 1997(1997), No. 22, pp 1-17.

### Stable multiple-layer stationary solutions of a semilinear parabolic
equation in two-dimensional domains

Arnaldo Simal do Nascimento

**Abstract:**

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.

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Arnaldo Simal do Nascimento

Universidade Federal de Sao Carlos, D.M.;
13565-905 - Sao Carlos, S.P. Brazil

e-mail: dasn@power.ufscar.br

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