On the local existence and blow-up solutions to a quasi-linear bi-hyperbolic equation with dynamic boundary conditions

This note aims to study the existence of the local solutions and derive a blow-up result for a quasi-linear bi-hyperbolic equation with dynamic boundary conditions. We use the maximal monotone operator theory to demonstrate the solution’s local well-posedness, and a concavity method to establish the...

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Published in:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2024-12, Vol.12, p.100925, Article 100925
Main Authors: Desova, Begüm Çalışkan, Polat, Mustafa
Format: Article
Language:English
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Bi-hyperbolic quasi-linear equations
Blow-up
Dynamic boundary condition
Maximal monotone operator theory
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description This note aims to study the existence of the local solutions and derive a blow-up result for a quasi-linear bi-hyperbolic equation with dynamic boundary conditions. We use the maximal monotone operator theory to demonstrate the solution’s local well-posedness, and a concavity method to establish the blow-up result.
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subjects Bi-hyperbolic quasi-linear equations
Blow-up
Dynamic boundary condition
Maximal monotone operator theory
title On the local existence and blow-up solutions to a quasi-linear bi-hyperbolic equation with dynamic boundary conditions
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