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Asymptotic stability via the Krein-Rutman theorem for singularly perturbed parabolic periodic dirichlet problems |
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| Authors: | N. N. Nefedov L. Recke K. R. Schneider |
| Affiliation: | 1. Faculty of Physics, M.V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia 2. Institut für Mathematik, Humboldt-Universit?t zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany 3. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany |
| Abstract: | We consider singularly perturbed semilinear parabolic periodic problems and assume the existence of a family of solutions. We present an approach to establish the exponential asymptotic stability of these solutions by means of a special class of lower and upper solutions. The proof is based on a corollary of the Krein-Rutman theorem. |
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