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

Abstract

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.

Keywords

• Maximal monotone operator theory
• Bi-hyperbolic quasi-linear equations
• Blow-up
• Dynamic boundary condition