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Research Article | Open Access

Existence, uniqueness, and blow-up analysis of a quasi-linear bi-hyperbolic equation with dynamic boundary conditions

Begüm Çalışkan Desova1( ), Mustafa Polat2
Department of Information Security Technology, Yeditepe University, Atasehir 34755, Turkey
Department of Mathematics, Yeditepe University, Atasehir 34755, Turkey
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Abstract

For this study, we investigate the existence and uniqueness of local solutions and derive a blow-up solution for a quasi-linear bi-hyperbolic equation under dynamic boundary conditions. We utilize the contraction mapping concept to demonstrate the solution's local well-posedness and employ a concavity approach to establish the blow-up result.

Keywords

wave equationlocal existenceblow-upcontraction mapping principle

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Electronic Research Archive
Volume 32 Issue 5,
May 2024
Pages 3363-3376
DOI: 10.3934/era.2024155

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Desova BÇ, Polat M. Existence, uniqueness, and blow-up analysis of a quasi-linear bi-hyperbolic equation with dynamic boundary conditions. Electronic Research Archive, 2024, 32(5): 3363-3376. https://doi.org/10.3934/era.2024155

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Received: 09 March 2024
Revised: 28 April 2024
Accepted: 07 May 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

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