Stable Multiple-layer Stationary Solutions of a Semilinear Parabolic Equation in Two-dimensional Domains
Nascimento, Arnaldo Simal do
Southwest Texas State University, Department of Mathematics
We use Γ-convergence to prove existence of stable multiple-layer stationary solutions (stable patterns) to a reaction-diffusion equation. Given nested simple closed curves in ℝ2, 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.
Diffusion equation, Gamma-convergence, Transition layers, Stable equilibria
Nascimento, A. S. (1997). Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains. <i>Electronic Journal of Differential Equations 1997</i>(22), pp. 1-17.
Attribution 4.0 International