Abstract
Using among other tools an approach based on the variational concept of Г-convergence, we manage to prove existence as well as stability and exhibit the geometric structure of a family of stationary solutions of a semilinear diffusion equation. The existence of these stable stationary solutions is solely due to suitable oscillations of the functions characterizing the spatial inhomogeneities involved in the problem. In particular, these oscillations depend on the signed curvature of a level curve of the square root of the product of these functions.
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Dedicated to the memory of R. Mañé
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Simal Nascimento, A. Stable stationary solutions induced by spatial inhomogeneity via Г-convergence. Bol. Soc. Bras. Mat 29, 75–97 (1998). https://doi.org/10.1007/BF01245869
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DOI: https://doi.org/10.1007/BF01245869