We study the asymptotic behavior of a linear elastic medium with a boundary condition with memory. By introducing a boundary free energy, we prove that, if the memory kernel $lambda$ exponentially decays and the domain is strongly star shaped, then the energy exponentially decays. We also prove that the exponential decay of $lambda$ is a necessary condition for the exponential decay of the solution.
C.A. Bosello, B. Lazzari, R. Nibbi (2007). A viscous boundary condition with memory in linear elasticity. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 45, 94-110 [10.1016/j.ijengsci.2006.07.013].
A viscous boundary condition with memory in linear elasticity
BOSELLO, CARLO ALBERTO;LAZZARI, BARBARA;NIBBI, ROBERTA
2007
Abstract
We study the asymptotic behavior of a linear elastic medium with a boundary condition with memory. By introducing a boundary free energy, we prove that, if the memory kernel $lambda$ exponentially decays and the domain is strongly star shaped, then the energy exponentially decays. We also prove that the exponential decay of $lambda$ is a necessary condition for the exponential decay of the solution.File in questo prodotto:
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