Local existence and lower bound of blow-up time to a cauchy problem of a coupled nonlinear wave equations

Mohammad Kafini; Shadi Al-Omari

doi:10.3934/math.2021526

Local existence and lower bound of blow-up time to a cauchy problem of a coupled nonlinear wave equations

Mohammad Kafini
, Shadi Al-Omari^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we consider a Cauchy problem of a coupled linearly-damped wave equations with nonlinear sources. In the whole space, we establish the local existence and show that there are solutions with negative initial energy that blow up in a finite time. Moreover, under some conditions on the initial data, we estimate a lower bound of that time.

Original language	English
Pages (from-to)	9059-9074
Number of pages	16
Journal	AIMS Mathematics
Volume	6
Issue number	8
DOIs	https://doi.org/10.3934/math.2021526
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2021 the Author(s), licensee AIMS Press.

Keywords

Blow up
Cauchy problem
Lower bound
Negative initial energy
Nonlinear source

ASJC Scopus subject areas

General Mathematics

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10.3934/math.2021526

Cite this

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title = "Local existence and lower bound of blow-up time to a cauchy problem of a coupled nonlinear wave equations",

abstract = "In this paper, we consider a Cauchy problem of a coupled linearly-damped wave equations with nonlinear sources. In the whole space, we establish the local existence and show that there are solutions with negative initial energy that blow up in a finite time. Moreover, under some conditions on the initial data, we estimate a lower bound of that time.",

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AU - Al-Omari, Shadi

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N2 - In this paper, we consider a Cauchy problem of a coupled linearly-damped wave equations with nonlinear sources. In the whole space, we establish the local existence and show that there are solutions with negative initial energy that blow up in a finite time. Moreover, under some conditions on the initial data, we estimate a lower bound of that time.

AB - In this paper, we consider a Cauchy problem of a coupled linearly-damped wave equations with nonlinear sources. In the whole space, we establish the local existence and show that there are solutions with negative initial energy that blow up in a finite time. Moreover, under some conditions on the initial data, we estimate a lower bound of that time.

KW - Blow up

KW - Cauchy problem

KW - Lower bound

KW - Negative initial energy

KW - Nonlinear source

UR - https://www.scopus.com/pages/publications/85108223967

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DO - 10.3934/math.2021526

M3 - Article

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JF - AIMS Mathematics

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ER -

Local existence and lower bound of blow-up time to a cauchy problem of a coupled nonlinear wave equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this