Global attractors for porous elastic system with memory and nonlinear frictional damping

This paper is concerned with the long‐time behavior of a porous‐elastic system with infinite memory and nonlinear frictional damping. We prove that the dynamical system generated by the solutions of the equations is dissipative, only under the basic conditions (for the well‐posedness) on the memory...

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Published inMathematical methods in the applied sciences Vol. 47; no. 2; pp. 600 - 620
Main Authors Duan, Yu‐Ying, Xiao, Ti‐Jun
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.01.2024
Subjects
Attractors (mathematics)
Damping
Dynamical systems
Elastic systems
frictional damping
global attractor
memory effect
porous elastic system
Smoothness
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Summary:This paper is concerned with the long‐time behavior of a porous‐elastic system with infinite memory and nonlinear frictional damping. We prove that the dynamical system generated by the solutions of the equations is dissipative, only under the basic conditions (for the well‐posedness) on the memory kernel g$$ g $$ and the frictional damping h$$ h $$. Further, we come up with a condition on g$$ g $$, being more general than the usual one g′(t)≤−cg(t)$$ {g}^{\prime }(t)\le - cg(t) $$ (with a positive constant c$$ c $$), under which we prove the asymptotic smoothness and quasi‐stability (the latter needs some stronger condition on h$$ h $$) of the dynamical system. Accordingly, we obtain the existence of a global attractor and show the finite dimensionality of the attractor.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9672