Control problem with a point source of heat used as a controller
The authors consider the problem of control of a heat equation boundary-value problem with two and three spatial variables. The problem is of the Dirichlet type with homogeneous boundary conditions. The control is the heat source and the source of cold both moving along continuous curves (being also parts of a solution). Both controls are almost point sources, i.e. they are described by approximations to the Dirac \(\delta\) function. In the first problem solved in the paper the object function is supremum over the time segment of the \(L_2\) discrepancy between the desired and the actual temperature distributions. In the second problem the object is to obtain the given temperature distribution in the end. One more solved problem is to obtain the given distribution by controlling the flux at the boundary for the heat problem with temperature sink. The article is very short and contains only the theorems with no proofs.
scientific article; zbMATH DE number 5905519