Fractal dimension of global attractors for a Kirchhoff wave equation with a strong damping and a memory term

Article type: Research Article

Authors: Qin, Yuming^{a; b; *} | Wang, Hongli^a | Yang, Bin^c

Affiliations: [a] Department of Mathematics, Donghua University, Shanghai, 201620, P.R. China | [b] Insitute of Nonlinear Science, Donghua University, Shanghai, 201620, P.R. China | [c] College of Information Science and Technology, Donghua University, Shanghai, 201620, P.R. China

Correspondence: [*] Corresponding author. E-mail: yuming@dhu.edu.cn.

Abstract: This paper is concerned with the dimension of the global attractors for a time-dependent strongly damped subcritical Kirchhoff wave equation with a memory term. A careful analysis is required in the proof of a stabilizability inequality. The main result establishes the finite dimensionality of the global attractor.

Keywords: Fractal dimension, subcritical case, Kirchhoff wave equation, global attractor, stabilizability inequality

DOI: 10.3233/ASY-231881

Journal: Asymptotic Analysis, vol. 137, no. 1-2, pp. 85-95, 2024