Abstract
Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.
Highlights
In this paper, we are interested in the long-time behavior of the coupled system of wave equations given by utt − ∆u +(−∆)α ut + g = f (u, v) + εh, in Ω × R+, vtt∆v (−∆)α vt + g = f u=v=, on ∂Ω × R+, (1.1) u( )=u, ut(
In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces
Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved
Summary
We are interested in the long-time behavior of the coupled system of wave equations given by utt. By employing nonlinear semigroups and the theory of monotone operators, the authors obtained several results on the existence of local and global weak solutions, and uniqueness of weak solutions They proved that such unique solutions depend continuously on the initial data. Our main interest in this paper is to study the long-time behavior of the autonomous dynamical system generated by the nonlinear coupled system of wave equations (1.1). In this context, the concept of global attractor is a useful objective to learn the dynamical behavior of a dynamical system [5, 8, 21, 29, 33, 44, 45].
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