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

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 inte grable. 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.

 Fuente: Communications on Pure and Applied Analysis, 2025, 24(4), 482-506

 Publisher: AIMS Press

 Publication date: 01/04/2025

 No. of pages: 25

 Publication type: Article

 DOI: 10.3934/cpaa.2025002

 ISSN: 1553-5258,1534-0392

 Spanish project: PID2020-114837GB-I00

 Publication Url: https://doi.org/10.3934/cpaa.2025002

Authorship

KARL KUNISCH