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Stability aspects in strain gradient theory of thermoelasticity with mass diffusion
Author(s) -
Aouadi Moncef,
Dhaba Amr Ramadan El,
Ghaleb Ahmed F.
Publication year - 2018
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.201800043
Subject(s) - thermoelastic damping , isotropy , exponential stability , diffusion , work (physics) , nonlinear system , mathematical analysis , stability (learning theory) , mathematics , heat equation , semigroup , classical mechanics , thermal , physics , thermodynamics , computer science , quantum mechanics , machine learning
This article is concerned with a strain gradient theory for thermoelastic diffusion materials. The work is motivated by the recent interest in the study of gradient theories and increasing use of materials which possess thermal and mass diffusion variations. First, we establish the basic equations of the nonlinear strain gradient theory for thermoelastic diffusion materials. Then, we deduce the constitutive equations for isotropic chiral thermoelastic diffusion materials. With the help of the semigroup theory of linear operators, we prove the well‐posedness of the problem and the asymptotic behavior of the solutions. The exponential stability is proved for the one‐dimensional problem by a spectral method.