@article{10902/15352,
year = {2018},
url = {http://hdl.handle.net/10902/15352},
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.},
organization = {The first two authors were partially supported by the Spanish Ministerio de Economía y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P. The third author was supported by the collaborative research center SFB 910, TU Berlin, project B6.},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Control and Optimization, 2018, 56(6), 4434-4460},
title = {Measure control of a semilinear parabolic equation with a nonlocal time delay},
author = {Casas Rentería, Eduardo and Mateos Alberdi, Mariano and Tröltzsch, Fredi},
}