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Volume 39, Issue 2
Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping

Wenjie Gao, Xiaolei Li & Chunpeng Wang

DOI: 10.4208/cmr.2022-0060

Commun. Math. Res., 39 (2023), pp. 190-208.

Published online: 2023-04

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  • 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.

  • Keywords

Convergence rate, energy estimate, non-autonomous damping.

  • AMS Subject Headings

35L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-190, author = {Gao , WenjieLi , Xiaolei and Wang , Chunpeng}, title = {Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {2}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0060}, url = {http://global-sci.org/intro/article_detail/cmr/21544.html} }
TY - JOUR T1 - Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping AU - Gao , Wenjie AU - Li , Xiaolei AU - Wang , Chunpeng JO - Communications in Mathematical Research VL - 2 SP - 190 EP - 208 PY - 2023 DA - 2023/04 SN - 39 DO - http://doi.org/10.4208/cmr.2022-0060 UR - https://global-sci.org/intro/article_detail/cmr/21544.html KW - Convergence rate, energy estimate, non-autonomous damping. AB -

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.

Gao , WenjieLi , Xiaolei and Wang , Chunpeng. (2023). Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping. Communications in Mathematical Research . 39 (2). 190-208. doi:10.4208/cmr.2022-0060
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