Error estimates for semilinear parabolic control problems in the absence of Tikhonov term

Abstract: In this paper, we analyze optimal control problems of semilinear parabolic equations, where the controls are distributed and depend only on time. Box constraints for the controls are imposed and the cost functional does not involve the control itself, only the associated state. We prove second order optimality conditions for local strong minimizers, which are used to derive error estimates in the numerical approximation. First we estimate the difference between the discrete and continuous optimal states. In the last part, under an additional assumption on the optimal adjoint state, we prove error estimates for the controls and improve the estimates for the states.

 Autoría: Casas E., Mateos M., Rösch A.,

 Fuente: SIAM Journal on Control and Optimization, 2019, 57(4), 2515-2540

Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2019

Nº de páginas: 26

Tipo de publicación: Artículo de Revista

DOI: 10.1137/18M117220X

ISSN: 0363-0129,1095-7138

Proyecto español: MTM2014-57531-P ; MTM2017-83185-P