Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping
Year: 2023
Author: Wenjie Gao, Xiaolei Li, Chunpeng Wang
Communications in Mathematical Research , Vol. 39 (2023), Iss. 2 : pp. 190–208
Abstract
This paper concerns the convergence rate of solutions to a hyperbolic equation with $p(x)$-Laplacian operator and non-autonomous damping. We apply the Faedo-Galerkin method to establish the existence of global solutions, and then use some ideas from the study of second order dynamical system to get the strong convergence relationship between the global solutions and the steady solution. Some differential inequality arguments and a new Lyapunov functional are proved to show the explicit convergence rate of the trajectories.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0060
Communications in Mathematical Research , Vol. 39 (2023), Iss. 2 : pp. 190–208
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Convergence rate energy estimate non-autonomous damping.