Blow-up Dynamics of Higher Dimensional Klein-Gordon Equation with Nonminimal Coupling in Subcritical Case

Abstract

The aim of this present work is to study the blow-up dynamics and lifespanestimate for solution to higher dimensional Klein-Gordon Equation in subcritical case, in which1 < p < psc. We construct the equation of motion from the Lagrangian of Klein-Gordon withnon-minimal coupling, where the coupling interaction of the scalar field is proportional to thescalar curvature of the spacetime. The equation of motion has the form like nonlinear dampedwave equation with mass. The novelty of this work is the time dependent of nonlinear term. Weuse test function method to proof the lifespan estimate.