Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional Laplacian

TL;DR

This paper proves the existence, uniqueness, and stability of attractors for a 2D nonlinear hyperbolic-parabolic system with fractional Laplacian, including exponential attractors with finite fractal dimension.

Contribution

It establishes the upper semicontinuity of the attractor and introduces the existence of a finite-dimensional exponential attractor for the system.

Findings

Existence and uniqueness of global solutions

Upper semicontinuity of the attractor

Finite fractal dimension of the exponential attractor

Abstract

In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a two-dimensional nonlinear hyperbolic-parabolic coupled system with fractional Laplacian. In addition, we also obtain the existence of an exponential attractor and show that this attractor has a finite fractal dimension in a space containing the phase space of the dynamical system.