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Stabilization in elastic solids with voids. (English) Zbl 1153.74016

Summary: We study the asymptotic behavior and analyticity of the solutions of one-dimensional poro-elasticity problem with thermal effect. Our main result is to prove the lack of exponential stability in the case of poro-elasticity with thermal effect when viscoelasticity is present. We prove the analyticity of the problem when a porous viscosity is present. We conclude by showing the impossibility of localization in time of the solutions in the isothermal case.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F05 Thermal effects in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74H30 Regularity of solutions of dynamical problems in solid mechanics
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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References:

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