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Pré-Publication, Document De Travail Année : 2009

On the Dirichlet boundary control of the heat equation with a final observation Part I: A space-time mixed formulation and penalization

Résumé

We are interested in the optimal control problem of the heat equation where the quadratic cost functional involves a final observation and the control variable is a Dirichlet boundary condition. We first prove that this problem is well-posed. Next, we check its equivalence with a fixed point problem for a space-time mixed system of parabolic equations. Finally, we introduce a Robin penalization on the Dirichlet boundary control for the mixed problem and analyze the convergence when the penalty parameter tends to zero.
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Dates et versions

hal-00400226 , version 1 (30-06-2009)

Identifiants

  • HAL Id : hal-00400226 , version 1

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Faker Ben Belgacem, Christine Bernardi, Henda El Fekih, Hajer Metoui. On the Dirichlet boundary control of the heat equation with a final observation Part I: A space-time mixed formulation and penalization. 2009. ⟨hal-00400226⟩
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