Related papers: The zero mass problem for Klein-Gordon equations
Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving…
We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov…
We prove a uniform weighted resolvent estimate for the massless Klein-Gordon operator on a curved spacetime which is sufficiently close to the Minkowski spacetime. This particularly implies the existence and H\"{o}lder continuity of the…
The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to…
The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can…
It has been known that if the initial data decay sufficiently fast at space infinity, then 1D Klein-Gordon equations with quadratic nonlinearity admit classical solutions up to time $e^{C/\epsilon^2}$ while $e^{C/\epsilon^2}$ is also the…
We prove the existence of time-periodic solutions to non-linear massive Klein-Gordon equations in Anti-de Sitter as well as their orbital stability over exponentially long times for certain values of the mass corresponding to completely…
We consider waves, which obey the semilinear Klein-Gordon equation, propagating in the Friedmann-Lemaitre-Robertson-Walker spacetimes. The equations in the de Sitter and Einstein-de Sitter spacetimes are the important particular cases. We…
In this thesis we explore S. Klainerman's proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985. We consider initial data with…
In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove $L^p-L^q$ estimates for the solutions…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the…
In this paper we calculate the Bondi mass of asymptotically flat spacetimes with interacting electromagnetic and scalar fields. The system of coupled Einstein-Maxwel-Klein-Gordon equations is investigated and corresponding field equations…
We show the existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric for small charge and mass of the field and small angular momentum of the black hole. The…
We investigate solutions of the Klein-Gordon equation in a class of five dimensional geometries presenting the same symmetries and asymptotic structure as the Gross-Perry-Sorkin monopole solution. Apart from globally regular metrics, we…
We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general, unrestrictive class of data, in particular, for Maxwell field of arbitrary size, and by a gauge…
Employing a transformation to hyperbolic space, we derive in a simple way exact solutions for the Klein-Gordon equation in an infinite square-well potential with one boundary moving at constant velocity, for the massless as well as for the…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
This paper establishes the global existence of solutions for a class of wave-Klein-Gordon coupled systems with specific nonlinearities in 3+1-dimensional Minkowski spacetime. The study demonstrates that imposing certain constraints on the…
For any sub-extremal Kerr spacetime with non-zero angular momentum, we find an open family of non-zero masses for which there exist smooth, finite energy, and exponentially growing solutions to the corresponding Klein-Gordon equation. If…