In this article, we derive a nonlinear strain gradient theory for porous thermoelastic diffusion materials taking into account micro-inertia effects as well. The elastic behavior is assumed to be consistent with the Mindlin Form II, whereas the thermal and mass diffusion behaviors are based on Fourier’s and Fick’s laws. The thermal and mass diffusion fields are influenced by the displacement, the porosity field and by some additional parameters that describe the strain gradient behavior. The equations of the linear theory are also obtained. Then, we use the semigroup approach to derive an existence and uniqueness result for the solutions to the noncentrosymmetric problem and to study their asymptotic behavior.
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