Optimal control of a nonhomogeneous Dirichlet boundary fractional diffusion equation

Authors:
René Dorville;Gisèle M. Mophou;Vincent S. Valmorin
Affiliations:
Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Institut d'Enseignement Supérieur de la Guyane, 2091 Route de Baduel 97337 CAYENNE, French Guiana;Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Campus Fouillole, 97159 Pointe-í-Pitre Guadeloupe (FWI), French Guiana;Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Campus Fouillole, 97159 Pointe-í-Pitre Guadeloupe (FWI), French Guiana
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

We study a nonhomogeneous Dirichlet boundary fractional diffusion equation in a bounded domain. The fractional time derivative is considered in the Riemann-Liouville sense. We first prove by transposition the existence and the uniqueness of the solution of the boundary fractional diffusion equation. Then under some appropriate assumptions on the closed convex set of the admissible controls, we obtain a decoupled optimality system.