Dynamics of a one-dimensional nonlinear poroelastic system weakly damped

In this paper, we study the long-time behavior of a nonlinear porous elasticity system. The system is subject to a viscoporous damping and a nonlinear source term which is locally Lipschitz and depends only on the volume fraction. The dynamical system associated with the solutions of the model is gr...

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Bibliographic Details
Published inZeitschrift für Analysis und ihre Anwendungen Vol. 43; no. 1; pp. 89 - 112
Main Authors Dos Santos, Manoel, Freitas, Mirelson, Ramos, Anderson
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2024
Subjects
Elasticity
Nonlinear theories
Porosity
Brazil
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Summary:In this paper, we study the long-time behavior of a nonlinear porous elasticity system. The system is subject to a viscoporous damping and a nonlinear source term which is locally Lipschitz and depends only on the volume fraction. The dynamical system associated with the solutions of the model is gradient, and under the hypothesis of equal speeds of propagation for the waves, we prove that it is also quasi-stable, which allows us to show the existence of a global attractor for the system, which is the main result of the paper.
ISSN:0232-2064
1661-4534
DOI:10.4171/zaa/1749