Title: Space-time $ L^\infty $-estimates for solutions of infinite horizon semilinear parabolic equations.
Authors: Casas, Eduardo; Kunisch, Karl
Abstract: This paper is devoted to proving $ L^\infty $-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.
Subjects: TIME perspective; SPACETIME; EQUATIONS
Publication: Communications on Pure & Applied Analysis, 2025, Vol 24, Issue 4, pN.PAG
ISSN: 1534-0392
Publication type: Academic Journal
DOI: 10.3934/cpaa.2025002

Space-time $ L^\infty $-estimates for solutions of infinite horizon semilinear parabolic equations.

Casas, Eduardo; Kunisch, Karl