Stability aspects in strain gradient theory of thermoelasticity with mass diffusion

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. 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.