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Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory

Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory EVOLUTION EQUATIONS AND doi:10.3934/eect.2015.4.241 CONTROL THEORY Volume 4, Number 3, September 2015 pp. 241{263 QUASI-STABILITY AND GLOBAL ATTRACTOR IN NONLINEAR THERMOELASTIC DIFFUSION PLATE WITH MEMORY Moncef Aouadi Ecole Nationale d'Ing enieurs de Bizerte Universit e de Carthage, Tunisia Alain Miranville Laboratoire de Math ematiques et Applications, Universit e de Poitiers Boulevard Marie et Pierre Curie 86962 Chasseneuil Futuroscope Cedex, France (Communicated by Igor Chueshov) Abstract. We analyse the longterm properties of a C semigroup describing the solutions to a nonlinear thermoelastic di usion plate, recently derived by Aouadi [1], where the heat and di usion ux depends on the past history of the temperature and the chemical potential gradients through memory ker- nels. First we prove the well-posedness of the initial-boundary-value problem using the C semigroup theory of linear operators. Then we show, without rotational inertia, that the thermal and chemical potential coupling is strong enough to guarantee the quasi-stability. By showing that the system is gra- dient and asymptotically compact, the existence of a global attractor whose fractal dimension is nite is proved. 1. Introduction. In this paper, we consider the following thermoelastic di usion plate equations with thermal memory e ects due to non-Fourier heat ux laws, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Evolution Equations & Control Theory Unpaywall

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Publisher
Unpaywall
ISSN
2163-2472
DOI
10.3934/eect.2015.4.241
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Abstract

EVOLUTION EQUATIONS AND doi:10.3934/eect.2015.4.241 CONTROL THEORY Volume 4, Number 3, September 2015 pp. 241{263 QUASI-STABILITY AND GLOBAL ATTRACTOR IN NONLINEAR THERMOELASTIC DIFFUSION PLATE WITH MEMORY Moncef Aouadi Ecole Nationale d'Ing enieurs de Bizerte Universit e de Carthage, Tunisia Alain Miranville Laboratoire de Math ematiques et Applications, Universit e de Poitiers Boulevard Marie et Pierre Curie 86962 Chasseneuil Futuroscope Cedex, France (Communicated by Igor Chueshov) Abstract. We analyse the longterm properties of a C semigroup describing the solutions to a nonlinear thermoelastic di usion plate, recently derived by Aouadi [1], where the heat and di usion ux depends on the past history of the temperature and the chemical potential gradients through memory ker- nels. First we prove the well-posedness of the initial-boundary-value problem using the C semigroup theory of linear operators. Then we show, without rotational inertia, that the thermal and chemical potential coupling is strong enough to guarantee the quasi-stability. By showing that the system is gra- dient and asymptotically compact, the existence of a global attractor whose fractal dimension is nite is proved. 1. Introduction. In this paper, we consider the following thermoelastic di usion plate equations with thermal memory e ects due to non-Fourier heat ux laws,

Journal

Evolution Equations & Control TheoryUnpaywall

Published: Jan 1, 2015

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