Well-posedness of semilinear strongly damped wave equations with fractional diffusion operators and $C^0$ potentials on arbitrary bounded domains
| Autor: | Joseph L. Shomberg |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
74H40
regularity Semigroup General Mathematics Nonlocal diffusion Mathematical analysis mild solutions uniqueness 35L20 Type (model theory) $C^0$ potential global well-posedness 35L71 semilinear strongly damped wave equation Nonlinear system Bounded function 35Q74 weak solutions Uniqueness Gevrey class Diffusion (business) Critical exponent Mathematics |
| Zdroj: | Rocky Mountain J. Math. 49, no. 4 (2019), 1307-1334 |
| Popis: | We examine the well-posedness of a strongly damped wave equation equipped with fractional diffusion operators. Ranges on the orders of the diffusion operators are determined in connection with global well-posedness of mild solutions or the global existence of weak solutions. Local existence proofs employ either semigroup methods or a Faedo-Galerkin scheme, depending on the type of solution sought. Mild solutions arising from semigroup methods are either analytic or of Gevrey class; the former produce a gradient system. We also determine the critical exponent for the nonlinear term depending on the orders of the fractional diffusion operators. Thanks to the nonlocal presentation of the fractional diffusion operators, we are able to work on arbitrary bounded domains. The nonlinear potential is only assumed to be continuous while satisfying a suitable growth condition. |
| Databáze: | OpenAIRE |
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