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Research Article | Open Access

Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition

Department of Mathematics, College of Science Al-Zulfi Majmaah University, Al-Majmaah 11952, Saudi Arabia
Mathematics Department, Sudan University of Science and Technology Khartoum, Sudan
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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.

Keywords

non-local interface conditionnonlinear hyperbolic PDEshomogenizationthe periodic unfolding method
CLC number: 35B27, 35K57

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 12093-12108
DOI: 10.3934/math.2023609

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Mohammed M. Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition. AIMS Mathematics, 2023, 8(5): 12093-12108. https://doi.org/10.3934/math.2023609

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Received: 09 January 2023
Revised: 13 March 2023
Accepted: 14 March 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)