Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition

Mogtaba Mohammed; Mogtaba Mohammed

doi:10.3934/math.2023609

AIMS Mathematics

2023, Volume 8, Issue 5: 12093-12108. doi: 10.3934/math.2023609

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Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition

Mogtaba Mohammed ^{1,2
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1.
Department of Mathematics, College of Science Al-Zulfi Majmaah University, Al-Majmaah 11952, Saudi Arabia
2.
Mathematics Department, Sudan University of Science and Technology Khartoum, Sudan

Received: 09 January 2023 Revised: 13 March 2023 Accepted: 14 March 2023 Published: 21 March 2023
MSC : 35B27, 35K57

In this work, we look at homogenization results for nonlinear hyperbolic problem with a non-local boundary condition. We use the periodic unfolding method to obtain a homogenized nonlinear hyperbolic equation in a fixed domain. Due to the investigation's peculiarity, the unfolding technique must be developed with special attention, creating an unusual two-scale model. We note that the non-local boundary condition caused a damping on the homogenized model.
- non-local interface condition,
- nonlinear hyperbolic PDEs,
- homogenization,
- the periodic unfolding method
Citation: Mogtaba Mohammed. Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition[J]. AIMS Mathematics, 2023, 8(5): 12093-12108. doi: 10.3934/math.2023609

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Abstract

In this work, we look at homogenization results for nonlinear hyperbolic problem with a non-local boundary condition. We use the periodic unfolding method to obtain a homogenized nonlinear hyperbolic equation in a fixed domain. Due to the investigation's peculiarity, the unfolding technique must be developed with special attention, creating an unusual two-scale model. We note that the non-local boundary condition caused a damping on the homogenized model.

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