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A theory of thermoelasticity with diffusion under Green‐Naghdi models
Author(s) -
Aouadi M.,
Lazzari B.,
Nibbi R.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300050
Subject(s) - semigroup , mathematics , impossibility , diffusion , nonlinear system , diffusion theory , mathematical analysis , anisotropy , linear system , physics , thermodynamics , optics , quantum mechanics , political science , law
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.