Nonexistence of global solutions to Klein-Gordon equations with variable coefficients power-type nonlinearities

Global Weak Entropy Solutions to Quasilinear Wave Equations of Klein{gordon and Sine{gordon Type

We establish the existence of global Lipschitz continuous weak entropy solutions to the Cauchy problem for a class of quasilinear wave equations with an external positional force. We prove the consistency and the convergence of uniformly bounded nite{diierence fractional step approximations. Therefore the uniform bound is shown to hold for globally Lipschitz continuous external forces.

Nonexistence of global solutions of a class of coupled nonlinear Klein-Gordon equations with nonnegative potentials and arbitrary initial energy

In the paper we consider the nonexistence of global solutions of the Cauchy problem for coupled Klein-Gordon equations of the form

solutions of the perturbed klein-gordon equations

this paper studies the perturbed klein-gordon equation by the aid of several methods of integrability. there are six forms of nonlinearity that are considered in this paper. the parameter domains are thus identified.

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Global Weak Solutions of the Relativistic Vlasov-klein-gordon System

We consider an ensemble of classical particles coupled to a KleinGordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the energy of the system is indefinite, and only for restr...