A theory of thermoelasticity with diffusion under Green-Naghdi models
Corresponding Author
M. Aouadi
Department of Mathematics and Computer Science, Institut Supérieur des Sciences Appliquées et de Technologie de Mateur, University of Carthage, Tunisia
Department of Mathematics and Computer Science, Institut Supérieur des Sciences Appliquées et de Technologie de Mateur, University of Carthage, TunisiaSearch for more papers by this authorB. Lazzari
Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
Search for more papers by this authorR. Nibbi
Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
Search for more papers by this authorCorresponding Author
M. Aouadi
Department of Mathematics and Computer Science, Institut Supérieur des Sciences Appliquées et de Technologie de Mateur, University of Carthage, Tunisia
Department of Mathematics and Computer Science, Institut Supérieur des Sciences Appliquées et de Technologie de Mateur, University of Carthage, TunisiaSearch for more papers by this authorB. Lazzari
Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
Search for more papers by this authorR. Nibbi
Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
Search for more papers by this authorAbstract
In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a nonlinear theory of thermoelasticity with diffusion of types II and III. This theory permits propagation of both thermal and diffusion waves at finite speeds. The equations of the linear theory are also obtained. With the help of the semigroup theory of linear operators we establish that the linear anisotropic problem is well posed and we study the asymptotic behavior of the solutions. Finally, we investigate the impossibility of the localization in time of solutions.
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