@article{10902/10481, year = {2017}, month = {1}, url = {http://hdl.handle.net/10902/10481}, abstract = {Optimal control problems with semilinear parabolic state equations are considered. The objective features one out of three different terms promoting various spatio-Temporal sparsity patterns of the control variable. For each problem, first-order necessary optimality conditions, as well as secondorder necessary and sufficient optimality conditions are proved. The analysis includes the case in which the objective does not contain the squared norm of the control.}, organization = {The first author was partially supported by Spanish Ministerio de Economía y Competitividad under the project MTM2011-22711.}, publisher = {EDP Sciences}, publisher = {ESAIM: Control, Optimisation and Calculus of Variations, 2017, 23 (1), 263-295}, title = {Analysis of spatio-temporally sparse optimal control problems of semilinear parabolic equations}, author = {Casas Rentería, Eduardo and Herzog, Roland and Wachsmuth, Gerd}, }