Delayed wave equation with logarithmic variable-exponent nonlinearity

Mohammad Kafini; Maher Noor; Mohammad Kafini; Maher Noor

doi:10.3934/era.2023150

Electronic Research Archive

2023, Volume 31, Issue 5: 2974-2993. doi: 10.3934/era.2023150

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Delayed wave equation with logarithmic variable-exponent nonlinearity

Mohammad Kafini ^{1,2
,
,},
Maher Noor ^2,3

1.
Department of Mathematics, The interdisciplinary research center in construction and building materials
2.
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
3.
Department of Mathematics, Dammam Community College

Received: 11 January 2023 Revised: 01 March 2023 Accepted: 07 March 2023 Published: 20 March 2023

A delayed nonlinear wave equation with variable exponents of logarithmic type is discussed in this paper. In the presence of the logarithmic nonlinear source, we established a global existence result under sufficient conditions on the initial data only without imposing the Sobolev Logarithmic Inequality. After that, we established global results of exponential and polynomial types according to the range values of the exponents. At the end, we give a numerical study that supports our theoretical results.
- decay,
- nonlinearly damped,
- delay time,
- variable exponent
Citation: Mohammad Kafini, Maher Noor. Delayed wave equation with logarithmic variable-exponent nonlinearity[J]. Electronic Research Archive, 2023, 31(5): 2974-2993. doi: 10.3934/era.2023150

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Abstract

A delayed nonlinear wave equation with variable exponents of logarithmic type is discussed in this paper. In the presence of the logarithmic nonlinear source, we established a global existence result under sufficient conditions on the initial data only without imposing the Sobolev Logarithmic Inequality. After that, we established global results of exponential and polynomial types according to the range values of the exponents. At the end, we give a numerical study that supports our theoretical results.

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