TY - GEN A1 - Hömberg, Dietmar A1 - Meyer, Christian A1 - Rehberg, Joachim A1 - Ring, Wolfgang T1 - Optimal control of the thermistor problem N2 - This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem. KW - Partial differential equations KW - optimal control problems KW - state constraints Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/544 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5441 ER -