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

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 equation
• local existence
• blow-up
• contraction mapping principle