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A note on existence of solutions to control problems of semilinear partial differential equations

Abstract: In this paper, we study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the corresponding state equations are well posed for controls in L2. However, it is well known that in the L2 framework the mappings involved in the control problem are not Frechet differentiable in general, which makes any analysis of the optimality conditions challenging. Nevertheless, we prove that every L2 optimal control belongs to L [infinito], and consequently standard optimality conditions are available.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Casas E., Wachsmuth D.,

 Fuente: SIAM Journal on Control and Optimization, 2023, 61(3), 1095-1112

Editorial: Society for Industrial and Applied Mathematics

 Fecha de publicación: 01/06/2023

Nº de páginas: 18

Tipo de publicación: Artículo de Revista

 DOI: 10.1137/22M1486418

ISSN: 0363-0129,1095-7138

 Proyecto español: PID2020-114837GB-I00