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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) under exclusive license to Università degli Studi di Ferrara 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
- ISSN
- 0430-3202
- eISSN
- 1827-1510
- DOI
- 10.1007/s11565-023-00466-5
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we consider a two-dimensional system of coupled nonlinear wave equations, one of which is subject to fractional Laplacian damping, the linear part of the system is based on Alabau-Boussouira et al. (J Evol Equ 2(2):127–150, 2002. https://doi.org/10.1007/s00028-002-8083-0). In addition, we consider the thermal effect according to Fourier’s Law acting on the system. We prove that the (two-parameters) dynamical system associates the solution of the system is quasi-stable and gradient, which implies the existence of a (two-parameters) family of compact global attractors. A result of regularity is also proven for the attractors, as well as showing that the family of attractors is upper semicontinuous, on the set of parameters.
Journal
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: May 30, 2023
Keywords: Coupled nonlinear wave equations; Fourier’s law; Quasi-stability; Attractors; Upper semicontinuity; Fractional Laplacian; 35B40; 35B41; 37L30