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

Tae Gab Ha; Seyun Kim

doi:10.3934/math.2023533

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

Tae Gab Ha^*
, Seyun Kim

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	10513-10528
Number of pages	16
Journal	AIMS Mathematics
Volume	8
Issue number	5
DOIs	https://doi.org/10.3934/math.2023533
State	Published - 2023

Keywords

energy decay
existence of solutions
nonlinear distributed delay
wave equations

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.3934/math.2023533

Cite this

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

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 = "energy decay, existence of solutions, nonlinear distributed delay, wave equations",

author = "Ha, \{Tae Gab\} and Seyun Kim",

note = "Publisher Copyright: {\textcopyright} 2023 the Author(s), licensee AIMS Press. is an open access article distributed under.",

year = "2023",

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TY - JOUR

T1 - Existence and energy decay rate of the solutions for the wave equation with a nonlinear distributed delay

AU - Ha, Tae Gab

AU - Kim, Seyun

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - energy decay

KW - existence of solutions

KW - nonlinear distributed delay

KW - wave equations

UR - https://www.scopus.com/pages/publications/85149258283

U2 - 10.3934/math.2023533

DO - 10.3934/math.2023533

M3 - Journal article

AN - SCOPUS:85149258283

SN - 2473-6988

VL - 8

SP - 10513

EP - 10528

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 5

ER -

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

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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