Global Existence And Growth Of Solutions To Coupled Degeneratly Damped Klein-Gordon Equations

Global Existence for Coupled Systems of Nonlinear Wave and Klein-Gordon Equations in Three Space Dimensions

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coup...

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.

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

Existence and Multiplicity of Solutions for Nonhomogeneous Klein-gordon-maxwell Equations

This article concerns the nonhomogeneous Klein-Gordon-Maxwell equation −∆u+ u− (2ω + φ)φu = |u|p−1u+ h(x), in R, ∆φ = (ω + φ)u, in R, where ω > 0 is constant, p ∈ (1, 5). Under appropriate assumptions on h(x), the existence of at least two solutions is obtained by applying the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.