Dirichlet Boundary Control of Semilinear Parabolic Equations Part 2: Problems with Pointwise State Constraints

Journal Article · Mon Jul 01 00:00:00 EDT 2002 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-001-0036-4· OSTI ID:21067493

Arada, N; fr, raymond@mip ups-tlse

This paper is the continuation of the paper 'Dirichlet boundary control of semilinear parabolic equations. Part 1: Problems with no state constraints'. It is concerned with an optimal control problem with distributed and Dirichlet boundary controls for semilinear parabolic equations, in the presence of pointwise state constraints. We first obtain approximate optimality conditions for problems in which state constraints are penalized on subdomains. Next by using a decomposition theorem for some additive measures (based on the Stone-Cech compactification), we pass to the limit and recover Pontryagin's principles for the original problem.

• OSTI ID: 21067493
• Journal Information: Applied Mathematics and Optimization, Vol. 45, Issue 2; Other Information: DOI: 10.1007/s00245-001-0036-4; Copyright (c) Inc. 2001 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPACTIFICATION
DIRICHLET PROBLEM
EQUATIONS
OPTIMAL CONTROL
SPACE-TIME