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1	Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations Malanowski, Kazimierz, Tröltzsch, Fredi 30 October 1998 (has links) (PDF) A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong. optimal control semilinear parabolic equations Lipschitz stability supremum norm MSC 49K20 MSC 49K40 ddc:510
2	Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations Tröltzsch, F. 30 October 1998 (has links) (PDF) We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm. Boundary control distributed control linear parabolic equation control constraints Lipschitz continuity supremum norm MSC 49K20 MSC 49K40 ddc:510
3	Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations Malanowski, Kazimierz, Tröltzsch, Fredi 30 October 1998 (has links) A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong. info:eu-repo/classification/ddc/510 ddc:510 optimal control semilinear parabolic equations Lipschitz stability supremum norm MSC 49K20 MSC 49K40
4	Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations Tröltzsch, F. 30 October 1998 (has links) We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm. info:eu-repo/classification/ddc/510 ddc:510 Boundary control distributed control linear parabolic equation control constraints Lipschitz continuity supremum norm MSC 49K20 MSC 49K40

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