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Optimal control of semilinear parabolic equations with non-smooth pointwise-integral control constraints in time-space

Abstract: This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form llu(t)ll L1(omega) >= G for t E (0, T ). This limits the total control that can be applied to the system at any instant of time. The L1-norm of the constraint leads to sparsity of the control in space, for the time instants when the constraint is active. Due to the non-smoothness of the constraint, the analysis of the control problem requires new techniques. Existence of a solution, first and second order optimality conditions, and regularity of the optimal control are proved. Further, stability of the optimal controls with respect to G is investigated on the basis of different second order conditions.

 Autoría: Casas E., Kunisch K.,

 Fuente: Applied Mathematics and Optimization, 2022, 85(1), 12

Editorial: Springer

 Fecha de publicación: 01/02/2022

Nº de páginas: 40

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00245-022-09850-7

ISSN: 0095-4616,1432-0606

 Proyecto español: MTM2017-83185-P

Url de la publicación: https://doi.org/10.1007/s00245-022-09850-7