GLOBAL EXISTENCE AND BLOW-UP FOR ONE-DIMENSIONAL WAVE EQUATION WITH WEIGHTED EXPONENTIAL NONLINEARITY

Thanaa Alarfaj; Lulwah Al-Essa; Fatimah Alkathiri; Mohamed Majdoub

doi:10.11948/20220305

2023 Volume 13 Issue 2

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Thanaa Alarfaj, Lulwah Al-Essa, Fatimah Alkathiri, Mohamed Majdoub. GLOBAL EXISTENCE AND BLOW-UP FOR ONE-DIMENSIONAL WAVE EQUATION WITH WEIGHTED EXPONENTIAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 1014-1026. doi: 10.11948/20220305

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Thanaa Alarfaj, Lulwah Al-Essa, Fatimah Alkathiri, Mohamed Majdoub. GLOBAL EXISTENCE AND BLOW-UP FOR ONE-DIMENSIONAL WAVE EQUATION WITH WEIGHTED EXPONENTIAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 1014-1026. doi: 10.11948/20220305

GLOBAL EXISTENCE AND BLOW-UP FOR ONE-DIMENSIONAL WAVE EQUATION WITH WEIGHTED EXPONENTIAL NONLINEARITY

1.
Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi Arabia
2.
Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia

Corresponding author: Email: mmajdoub@iau.edu.sa (M. Majdoub)

Abstract

Abstract

We consider the initial value problem for a one-dimensional wave equation with weighted exponential nonlinearity. We show global existence for small amplitude initial data. We also prove that blow-up in finite time occurs if the initial data are localized and the initial velocity being on the average positive.
- Nonlinear wave equation /
- blow-up /
- differential inequalities /
- Hammerstein-type Volterra integral equations
MSC: 35K58, 35A01, 35B40, 46E30

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References

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