We will systematically investigate so-called sparse control approaches for problems governedby quasilinear partial differential equations (PDEs). Many practical optimization problems can be described by control problems consisting of such a (often highly nonlinear) PDE and a so-called objective functional. For certain functionals it is known from the control of simpler linear and semilinear PDEs that rather small and simple, i.e. sparse, geometric structures often emerge as support of an optimal solution.Such sparse structures are also well-suited for practical applications. We will attack the additional mathematical challenges that appear in the context of optimization of quasilinear equations.
DFG Programme
Collaborative Research Centres
