151. Second order optimality conditions for optimal control of quasilinear parabolic equations
- Author
-
Lucas Bonifacius and Ira Neitzel
- Subjects
Quadratic growth ,Control and Optimization ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Order (ring theory) ,Boundary (topology) ,Optimal control ,Differential operator ,01 natural sciences ,Parabolic partial differential equation ,010101 applied mathematics ,Nonlinear system ,Boundary value problem ,0101 mathematics ,Mathematics - Abstract
We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality conditions are derived. The latter leads to a quadratic growth condition without two-norm discrepancy. Furthermore, maximal parabolic regularity of the state equation in Bessel-potential spaces \begin{document} $H_D^{-\zeta,p}$ \end{document} with uniform bound on the norm of the solution operator is proved and used to derive stability results with respect to perturbations of the nonlinear differential operator.
- Published
- 2018