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

Mohammad Kafini; Shadi Al-Omari; Mohammad Kafini; Shadi Al-Omari

doi:10.3934/math.2021526

AIMS Mathematics

2021, Volume 6, Issue 8: 9059-9074. doi: 10.3934/math.2021526

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

Mohammad Kafini ¹,
Shadi Al-Omari ^{2
,
,}

1.
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, IR Center of Construction and Building Materials, Dhahran 31261, Saudi Arabia
2.
Preparatory Year Program - Department of Mathematics, King Fahd University of Petroleum and Minerals, IR Center of Construction and Building Materials, Dhahran 31261, Saudi Arabia

Received: 08 May 2021 Accepted: 11 June 2021 Published: 17 June 2021
MSC : 35B44, 35D30, 35L05, 35L15, 35L70

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.
- Cauchy problem,
- blow up,
- negative initial energy,
- nonlinear source,
- lower bound
Citation: Mohammad Kafini, Shadi Al-Omari. Local existence and lower bound of blow-up time to a Cauchy problem of a coupled nonlinear wave equations[J]. AIMS Mathematics, 2021, 6(8): 9059-9074. doi: 10.3934/math.2021526

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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.

References

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