On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up

Abstract

Abstract This paper deals with a hyperbolic-type equation with a logarithmic source term and dynamic boundary condition. Given convenient initial data, we obtained the local existence of a weak solution. Local existence results of solutions are obtained using the Faedo-Galerkin method and the Schauder fixed-point theorem. Additionally, under suitable assumptions on initial data, the lower bound time of the blow-up result is investigated.

Keywords

• Blow-up
• Dynamical boundary condition
• Existence
• Logarithmic nonlinearity
• Partial differential equations
• Mathematical operators