相关论文: Global existence of small amplitude solution to no…

In this paper, we study the long time behavior of energy solutions for a class of wave equation with time-dependent mass and speed of pro\-pagation. We introduce a classification of the potential term, which clarifies whether the solution…

In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the…

This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely on…

In this paper we present the power series solution of the Klein-Gordon equation in the spacetime background of a gravitational wave with amplitude that decays with distance from the source. The resulting solution describes the interaction…

In this paper, we prove the existence of global in time small data solutions of semilinear Klein-Gordon equations in space-time with a static Schwarzschild radius in the expanding universe.

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For a system of nonlinear Klein-Gordon equations, a systematic analysis of the time evolution for their spatially uniform solutions has been performed…

We consider the nonlinear massless wave equation belonging to some family of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We prove the global in time small data solutions for supercritical powers in the case of decelerating…

This paper considers the question of global in time existence and asymptotic behavior of small-data solutions of nonlinear dispersive equations with a real potential $V$. The main concern is treating nonlinearities whose degree is low…

We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…

We are concerned with the existence of global in time solutions to the Cauchy problem for semi-linear Klein-Gordon equations with memory-type dissipation in $\mathbb{R}^n$. In the first place, we consider the linearized equation: applying…

We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with…

We consider a system of two coupled non-linear Klein-Gordon equations. We show the existence of standing waves solutions and the existence of a Lyapunov function for the ground state.

We study the Klein-Gordon equation with general interaction term, which may be linear or nonlinear, and space-time dependent. The initial data is general, large and non-radial. We prove that global solutions are asymptotically given by a…

We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small…

In this paper, we establish a relation between two seemingly unrelated concepts for solving first-order hyperbolic quasilinear systems of partial differential equations in many dimensions. These concepts are based on a variant of the…

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a…

We consider Klein-Gordon equations with an external potential $V$ and a quadratic nonlinearity in $3+1$ space dimensions. We assume that $V$ is regular and decaying and that the (massive) Schr\"odinger operator $H=-\Delta+V+m^2$ has a…

We consider a U(1)-invariant nonlinear Klein-Gordon equation in dimension one or larger, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic…

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.

We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…