Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints

J.-P. Raymond; F. Tröltzsch

doi:10.3934/dcds.2000.6.431

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2000, Volume 6, Issue 2: 431-450. Doi: 10.3934/dcds.2000.6.431

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Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints

J.-P. Raymond^1, and
F. Tröltzsch^2,

1.
Laboratoire MIP, UMR 5640, Université Paul Sabatier, 31062 Toulouse Cedex 4
2.
Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz

Received: June 30, 1998

Revised: May 31, 1999

Published: March 2000

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Abstract

In this paper, optimal control problems for semilinear parabolic equations with distributed and boundary controls are considered. Pointwise constraints on the control and on the state are given. Main emphasis is laid on the discussion of second order sufficient optimality conditions. Sufficiency for local optimality is verified under different assumptions imposed on the dimension of the domain and on the smoothness of the given data.

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Mathematics Subject Classification: 49K20, 35J25.

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