Abstract
We study the energy decay of the solutions of a linear homogeneous anisotropic porous thermoelastic system in the context of Green and Naghdi model of type II with the following boundary condition with memory for the displacement \({{\bf T}(x,t)n(x) = -\gamma_0v(x,t) - \int_0^\infty \lambda(s)v^t(x,s) {{d}}s}\) . By introducing a boundary free energy, we prove that if the kernel λ exponentially decays in time, then also the energy exponentially decays when porosity viscosity is present.
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Aouadi, M., Lazzari, B. & Nibbi, R. Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation. Z. Angew. Math. Phys. 63, 961–973 (2012). https://doi.org/10.1007/s00033-012-0201-4
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DOI: https://doi.org/10.1007/s00033-012-0201-4