Spike controls for elliptic and parabolic PDEs
The authors use measures of minimal norm to control elliptic and parabolic equations. They show the sparsity of the optimal control. In the parabolic case they show that the solution of the optimization problem is a Borel measure supported in a set of null Lebesgue measure. ``In both cases, approximate controllability can be achieved efficiently by means of controls that are activated in some finite number of pointwise locations'' (from the abstract). The corresponding dual problems are also studied. Possible extensions of the obtained results and some open problems are pointed out.
scientific article; zbMATH DE number 6157692