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Research Article | Open Access

Existence and energy decay rate of the solutions for the wave equation with a nonlinear distributed delay

Tae Gab Ha( ), Seyun Kim
Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju 54896, Republic of Korea
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Abstract

This paper is concerned with the wave equation having a nonlinear distributed delay. First, we prove the local existence of the solutions by using the semigroup theory, where the source term is globally Lipschitz. Next, we establish the global existence of solutions and the energy decay result under the local Lipschitz source and suitable conditions on the initial data.

Keywords

wave equationsnonlinear distributed delayexistence of solutionsenergy decay
CLC number: 35A01, 35B35, 35B40, 35L05

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 10513-10528
DOI: 10.3934/math.2023533

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Cite this article:
Ha TG, Kim S. Existence and energy decay rate of the solutions for the wave equation with a nonlinear distributed delay. AIMS Mathematics, 2023, 8(5): 10513-10528. https://doi.org/10.3934/math.2023533

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Received: 07 December 2022
Revised: 20 February 2023
Accepted: 22 February 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)