Dirichlet Boundary Control of Semilinear Parabolic Equations Part 1: Problems with No State Constraints |
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Authors: | N Arada J -P Raymond |
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Institution: | (1) UMR CNRS MIP, Université Paul Sabatier, 31062 Toulouse cedex 4, France \{arada,raymond\}@mip.ups-tlse.fr, FR |
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Abstract: | This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence
of pointwise state constraints. The paper is divided into two parts. In the first part we define solutions of the state equation
as the limit of a sequence of solutions for equations with Robin boundary conditions. We establish Taylor expansions for solutions
of the state equation with respect to perturbations of boundary control (Theorem 5.2). For problems with no state constraints,
we prove three decoupled Pontryagin's principles, one for the distributed control, one for the boundary control, and the last
one for the control in the initial condition (Theorem 2.1). Tools and results of Part 1 are used in the second part to derive
Pontryagin's principles for problems with pointwise state constraints.
Accepted 12 July 2001. Online publication 21 December 2001. |
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Keywords: | , Dirichlet boundary controls, Semilinear parabolic equation, Pontryagin's principle, AMS Classification, 49K20,,,,,,93C20, 35K20, |
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