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

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

Thanaa Alarfaj
, Lulwah Al-Essa
, Fatimah Alkathiri
, Mohamed Majdoub^*

^*Corresponding author for this work

Mathematics Department

Imam Abdulrahman Bin Faisal University

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

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.

Original language	English
Pages (from-to)	1014-1026
Number of pages	13
Journal	Journal of Applied Analysis and Computation
Volume	13
Issue number	2
DOIs	https://doi.org/10.11948/20220305
State	Published - Apr 2023

Keywords

Ham-merstein-type Volterra integral equations
Nonlinear wave equation
blow-up
differential inequalities

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10.11948/20220305

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title = "GLOBAL EXISTENCE AND BLOW-UP FOR ONE-DIMENSIONAL WAVE EQUATION WITH WEIGHTED EXPONENTIAL NONLINEARITY",

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.",

keywords = "Ham-merstein-type Volterra integral equations, Nonlinear wave equation, blow-up, differential inequalities",

author = "Thanaa Alarfaj and Lulwah Al-Essa and Fatimah Alkathiri and Mohamed Majdoub",

year = "2023",

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doi = "10.11948/20220305",

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AU - Alarfaj, Thanaa

AU - Al-Essa, Lulwah

AU - Alkathiri, Fatimah

AU - Majdoub, Mohamed

PY - 2023/4

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N2 - 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.

AB - 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.

KW - Ham-merstein-type Volterra integral equations

KW - Nonlinear wave equation

KW - blow-up

KW - differential inequalities

UR - https://www.scopus.com/pages/publications/85152068719

U2 - 10.11948/20220305

DO - 10.11948/20220305

M3 - Article

AN - SCOPUS:85152068719

SN - 2156-907X

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JO - Journal of Applied Analysis and Computation

JF - Journal of Applied Analysis and Computation

IS - 2

ER -

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

Abstract

Keywords

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