@article{10902/24444, year = {2022}, month = {2}, url = {http://hdl.handle.net/10902/24444}, 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(Ω) ≤ γ for t ∈ (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 γ is investigated on the basis of different second order conditions.}, organization = {Eduardo Casas was supported by MCIN/ AEI/10.13039/501100011033/ under research projects MTM2017-83185-P and PID2020-114837GB-I00. Karl Kunisch was supported by the ERC advanced Grant 668998 (OCLOC) under the EU’s H2020 research program.}, publisher = {Springer}, publisher = {Applied Mathematics and Optimization, 2022, 85(1), 12}, title = {Optimal control of semilinear parabolic equations with non-smooth pointwise-integral control constraints in time-space}, author = {Casas Rentería, Eduardo and Kunisch, Karl}, }