Approximate controllability of abstract nonsimple thermoelastic problem

Moncef  Aouadi; Taoufik  Moulahi

doi:10.3934/eect.2015.4.373

Article Contents

2015, Volume 4, Issue 4: 373-389. Doi: 10.3934/eect.2015.4.373

This issue Previous Article Next Article On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions

Approximate controllability of abstract nonsimple thermoelastic problem

Moncef Aouadi^1, and
Taoufik Moulahi^2,

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

Received: March 31, 2015

Revised: September 30, 2015

Published: November 2015

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Abstract

In this paper, an abstract nonsimple thermoelastic problem involving higher order gradients of displacement is considered with Dirichlet boundary conditions. We prove that the linear operator of the proposed system generates a strongly continuous semigroup which decays exponentially to zero. The optimal decay rate is determined explicitly by the physical parameters of the problem. Then we show the approximate controllability of the considered problem.

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Mathematics Subject Classification: Primary: 49K20; Secondary: 35B35.

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References

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