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2019 Well-posedness of semilinear strongly damped wave equations with fractional diffusion operators and $C^0$ potentials on arbitrary bounded domains
Joseph L. Shomberg
Rocky Mountain J. Math. 49(4): 1307-1334 (2019). DOI: 10.1216/RMJ-2019-49-4-1307

Abstract

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.

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Joseph L. Shomberg. "Well-posedness of semilinear strongly damped wave equations with fractional diffusion operators and $C^0$ potentials on arbitrary bounded domains." Rocky Mountain J. Math. 49 (4) 1307 - 1334, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1307

Information

Published: 2019
First available in Project Euclid: 29 August 2019

MathSciNet: MR3998923
zbMATH: 07104719
Digital Object Identifier: 10.1216/RMJ-2019-49-4-1307

Subjects:
Primary: 35L20, 35L71
Secondary: 35Q74, 74H40.

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 4 • 2019
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