# American Institute of Mathematical Sciences

June  2016, 5(2): 201-224. doi: 10.3934/eect.2016001

## Partial exact controllability for inhomogeneous multidimensional thermoelastic diffusion problem

 1 Ecole Nationale d'Ingénieurs de Bizerte, Université de Carthage, BP66, Campus Universitaire Menzel Abderrahman 7035 2 Faculté des Sciences de Bizerte, Jarzouna 7021, Université de Carthage, Tunisia

Received  January 2016 Revised  May 2016 Published  June 2016

The problem of stabilization and controllability for inhomogeneous multidimensional thermoelastic diffusion problem is considered for anisotropic material. By introducing a nonlinear feedback function on part of the boundary of the material, which is clamped along the rest of its boundary, we prove that the energy of the system decays to zero exponentially or polynomially. Both rates of decay are determined explicitly by the physical parameters. Via Russell's Controllability via Stabilizability" principle, we prove that the considered system is partially controllable by a boundary function determined explicitly.
Citation: Moncef Aouadi, Kaouther Boulehmi. Partial exact controllability for inhomogeneous multidimensional thermoelastic diffusion problem. Evolution Equations & Control Theory, 2016, 5 (2) : 201-224. doi: 10.3934/eect.2016001
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