Space-time L∞-estimates for solutions of infinite horizon semilinear parabolic equations

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URI: https://hdl.handle.net/10902/35316
ISSN: 1553-5258
ISSN: 1534-0392
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Autoría
Casas Rentería, EduardoAutoridad Unican; Kunisch, Karl
Fecha
2025-04
Derechos
© American Institute of Mathematical Sciences. This article has been accepted for publication in a revised form in Communications on Pure and Applied Analysis https://www.aimsciences.org/article/doi/10.3934/cpaa.2025002. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
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Communications on Pure and Applied Analysis, 2025, 24(4), 482-506
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AIMS Press
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Resumen/Abstract
This paper is devoted to proving L∞-estimates for the solution of semilinear parabolic equations. The uniform estimates are obtained on the infinite time interval under the assumption that the solution is square integrable. This setting is useful for stabilization problems formulated as optimal control problems. The inhomogenous forcing function are chosen as elements of anisotropic Lebesgue spaces. Different boundary conditions on bounded domains with a Lipschitz continuous boundary are investigated.
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