Mauro L. Santos, Mirelson M. Freitas, Ronal Q. Caljaro
Abstract:
In this article we consider a one-dimensional porous-elastic system
with nonlinear localized damping acting in an arbitrarily small region
of the interval under consideration. We prove the existence of a
smooth global attractor with finite fractal dimension
and the existence of exponential attractors via
quasi-stability theory recently proposed by Chueshov and Lasiecka.
We also prove the continuity of the attractors with respect to two
parameters in a residual dense set. Finally, we prove that the family
of global attractors is upper-semicontinuous with respect to small
perturbations of external forces. These aspects were not previously
considered for porous-elastic system with localized damping.
Submitted April 12, 2024. Published February 3, 2025.
Math Subject Classifications: 35B40, 35B41, 37L30, 35L75.
Key Words: Porous-elastic system; nonlinear localized damping; quasi-stability;
global attractor; upper-semicontinuity.
DOI: 10.58997/ejde.2025.11
Show me the PDF file (401 KB), TEX file for this article.
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Mauro L. Santos PhD Program in Mathematics Federal University of Pará Augusto Corrêa Street 01 Belém - PA, 66075-110, Brazil email: ls@ufpa.br |
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Mirelson M. Freitas Department of Mathematics University of Brasília Brasília-DF, 70910-900, Brazil email: mirelson.freitas@unb.br |
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Ronal Q. Caljaro PhD Program in Mathematics Federal University of Pará Augusto Corrêa Street 01 Belém--PA, 66075-110, Brazil email: ronalquispecaljaro@gmail.com |
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