Asymptotic behavior of the wave equation solution with nonlinear boundary damping and source term of variable exponent-type

Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Mohammad Kafini; Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Mohammad Kafini

doi:10.3934/math.20241479

AIMS Mathematics

2024, Volume 9, Issue 11: 30638-30654. doi: 10.3934/math.20241479

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Research article

Asymptotic behavior of the wave equation solution with nonlinear boundary damping and source term of variable exponent-type

1.
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2.
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received: 10 August 2024 Revised: 21 September 2024 Accepted: 12 October 2024 Published: 28 October 2024
MSC : 35A02, 35B35, 35B40, 35L20, 93D20

In this study, a nonlinear damped wave equation within a bounded domain was considered. We began by demonstrating the global existence of solutions through the application of the well-depth method. Following this, a general decay rate for the solutions was established using the multiplier method alongside key properties of convex functions. Notably, these results were derived without the imposition of restrictive growth assumptions on the frictional damping, making this work an improvement and extension of previous findings in the field.
- nonlinear wave equations,
- stability,
- boundary damping and source terms,
- variable exponent,
- multiplier and perturbed energy methods
Citation: Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Mohammad Kafini. Asymptotic behavior of the wave equation solution with nonlinear boundary damping and source term of variable exponent-type[J]. AIMS Mathematics, 2024, 9(11): 30638-30654. doi: 10.3934/math.20241479

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Abstract

In this study, a nonlinear damped wave equation within a bounded domain was considered. We began by demonstrating the global existence of solutions through the application of the well-depth method. Following this, a general decay rate for the solutions was established using the multiplier method alongside key properties of convex functions. Notably, these results were derived without the imposition of restrictive growth assumptions on the frictional damping, making this work an improvement and extension of previous findings in the field.

References

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