Blow-up Dynamics of Higher Dimensional Klein-Gordon Equation with Nonminimal Coupling in Subcritical Case
Mirda P. Wijayanto (1*) , Fiki T. Akbar (1,2), Bobby E. Gunara (1,2)

1) Theoretical High Energy Physics Research Group, Institut Teknologi Bandung,
Jl. Ganesha 10 Bandung 40132, Indonesia}
*mirda.prisma.wijayanto[at]students.itb.ac.id
2) Indonesian Center for Theoretical and Mathematical Physics (ICTMP),
Jl. Ganesha 10 Bandung 40132, Indonesia

Abstract

The aim of this present work is to study the blow-up dynamics and lifespan estimate for solution to higher dimensional Klein-Gordon Equation in subcritical case, in which 1<p<p_{sc}. We construct the equation of motion from the Lagrangian of Klein-Gordon with non-minimal coupling, where the coupling interaction of the scalar field is proportional to the scalar curvature of the spacetime. The equation of motion has the form like nonlinear damped wave equation with mass. The novelty of this work is the time dependent of nonlinear term. We use test function method to proof the lifespan estimate.

Keywords: Blow-up dynamics, Lifespan estimate, Nonlinear wave equation

Topic: Theoretical High Energy Physics