A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrarily positive initial energy

2007/02/07 by Wang, Yanjin
#35L05 #35L15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0702187

Abstract

In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form u_tt-Δu+m²u=f(u)amp; (t,x)∈ [0,T)×\Rⁿ. Here m≠ 0 and the nonlinear power f(u) satisfies some assumptions which will be stated later. We give a sufficient condition on the initial datum with arbitrarily high initial energy such that the solution of the above Klein-Gordon equation blows up in a finite time.

Related

• Criteria for finite time blow up for a system of Klein-Gordon equations
• Nonexistence of global solutions of a class of coupled nonlinear Klein-Gordon equations with nonnegative potentials and arbitrary initial energy
• Long time dynamics for damped Klein-Gordon equations
• The critical power of short pulse initial data on the global existence or blowup of smooth solutions to 3-D semilinear Klein-Gordon equations
• The semilinear Klein-Gordon equation in de Sitter spacetime