Partial exact controllability for inhomogeneous multidimensional thermoelastic diffusion problem

Moncef  Aouadi; Kaouther  Boulehmi

doi:10.3934/eect.2016001

Article Contents

2016, Volume 5, Issue 2: 201-224. Doi: 10.3934/eect.2016001

This issue Previous Article Next Article Blowup and ill-posedness results for a Dirac equation without gauge invariance

Partial exact controllability for inhomogeneous multidimensional thermoelastic diffusion problem

Moncef Aouadi^1, and
Kaouther Boulehmi^2,

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

Received: December 31, 2015

Revised: April 30, 2016

Published: May 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B37; Secondary: 35B35.

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