A potential well theory for the wave equation with nonlinear source and boundary damping terms. (English) Zbl 1016.35048

The paper deals with local existence, blow-up and global existence for the weak solutions of a semilinear wave equation \(u_{tt}-\triangle u=|u|^{p-2}u\) with a nonlinear boundary damping on a part of the boundary.


35L70 Second-order nonlinear hyperbolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35L05 Wave equation
35B45 A priori estimates in context of PDEs