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

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

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 co...

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Bibliographic Details
Published in:Electronic research archive Vol. 32; no. 5; pp. 3363 - 3376
Main Authors: Desova, Begüm Çalışkan, Polat, Mustafa
Format: Journal Article
Language:English
Published: AIMS Press 01-01-2024
Subjects:
blow-up
contraction mapping principle
local existence
wave equation
Online Access:Get full text
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Description
Summary: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.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2024155