Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
| Autor: | Juraj Húska, M. V. Safonov, Peter Poláčik |
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| Rok vydání: | 2007 |
| Předmět: |
Dirichlet problem
Floquet theory Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Lipschitz continuity 01 natural sciences Parabolic partial differential equation Exponential function 010101 applied mathematics Exponential growth Bundle Bounded function 0101 mathematics Mathematical Physics Analysis Mathematics |
| Zdroj: | Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 24:711-739 |
| ISSN: | 1873-1430 0294-1449 |
| DOI: | 10.1016/j.anihpc.2006.04.006 |
| Popis: | We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain. |
| Databáze: | OpenAIRE |
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