Semilinear parabolic systems with hysteresis: Hadamard differentiability of the solution operator and optimal control
Christian Münch · 2018
This thesis considers semilinear parabolic evolution systems with hysteresis. We prove resolvent estimates for elliptic operators and show well-posedness, Lipschitz continuity and Hadamard differentiability of the solution operator. The results are applied in optimal control of hysteresis-reaction-diffusion systems. The control acts distributed or on a part of the boundary. We show first order necessary optimality conditions, regularity results for the adjoint system and prove higher regularity of optimal solutions. Finally, we analyze a perturbed control problem when the set of controls is restricted.