Measure control of a semilinear parabolic equation with a nonlocal time delay

Abstract: We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a nondifferentiable term with the measure norm of the control. Existence, uniqueness, and regularity of the solution of the state equation, as well as differentiability properties of the control-to-state operator are obtained. Next, we provide first order optimality conditions for local solutions. Finally, the control space is suitably discretized and we prove convergence of the solutions of the discrete problems to the solutions of the original problem. Several numerical examples are included to illustrate the theoretical results.

 Autoría: Casas E., Mateos M., Tröltzsch F.,

 Fuente: SIAM Journal on Control and Optimization, 2018, 56(6), 4434-4460

Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2018

Nº de páginas: 27

Tipo de publicación: Artículo de Revista

DOI: 10.1137/17M1157362

ISSN: 0363-0129,1095-7138

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