Work

Asymptotic behavior of the Boussinesq equation with nonlocal weak damping and arbitrary growth nonlinear function

Year: 2024

Type: article

Abstract: In this paper, we consider the asymptotic behavior of the Boussinesq equation with nonlocal weak damping when the nonlinear function is arbitrary polynomial growth. We firstly prove the well‐posedness of solution by means of the monotone operator theory. At the same time, we obtain the dissipative property of the dynamical system associated with the problem in the space and , respectively. After that, the asymptotic smoothness of the dynamical system and the further quasi‐stability are demonstrated by the energy reconstruction method. Finally, we show not only the existence of the finite global attractor but also the existence of the generalized exponential attractor.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10566

Authors: Qiaozhen Ma, Yichun Mo, Lulu Wang, Lijuan Yao

Institutions: Northwest Normal University, Lanzhou Jiaotong University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, National Natural Science Foundation of China

Award: 具有时间依赖系数的非线性耗散演化方程解的长期动力学研究