Blow-up results for systems of nonlinear Klein-Gordon equations with arbitrary positive initial energy

Abstract

The initial boundary value problem for a system of nonlinear Klein-Gordon equations in a bounded domain is considered. We prove the existence of local solutions by using a successive approximation method. Then, we show blow-up results with arbitrary positive initial energy by a concavity method. Also estimates for the lifespan of solutions are given.

Keywords

• Blow-up
• life span
• damping
• nonlinear
• wave equations
• Klein-Gordon equation