相关论文: Global Solutions of Multispeed Semilinear Klein-Go…
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…
In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, Preprint (2024), arXiv:2405.03242], for the…
In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of…
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…
H\"ormander proved global existence of solutions for sufficiently small initial data for scalar wave equations in $(1+4)-$dimensions of the form $\Box u = Q(u, u', u'')$ where $Q$ vanishes to second order and $(\partial_u^2 Q)(0,0,0)=0$.…
We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that…
For general nonlinear Klein-Gordon equations with dissipation we show that any finite energy radial solution either blows up in finite time or asymptotically approaches a stationary solution in $H^1\times L^2$. In particular, any global…
It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such result still holds for a certain class of…
In this paper, we study the asymptotic dynamics of global solutions to damped Klein-Gordon equations in inhomogeneous mediums (KGI). In the defocusing case, we prove for any initial data, the solution is globally define in forward time and…
On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing…
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 are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion are a system of coupled semilinear wave and Klein-Gordon…
We study the non-uniqueness sets for solutions to the Klein-Gordon equation in 1 space dimension, for solutions whose Fourier transform is a finite complex measure absolutely continuous with respect to arc length. We show that generally, in…
We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…
We discuss the Cauchy problem for a system of semilinear wave equations in three space dimensions with multiple wave speeds. Though our system does not satisfy the standard null condition, we show that it admits a unique global solution for…
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges…
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 consider the asymptotic behavior of small global-in-time solutions to a 1D Klein-Gordon equation with a spatially localized, variable coefficient quadratic nonlinearity and a non-generic linear potential. The purpose of this work is to…
We study the long-time behaviour of solutions to a one-dimensional linear Klein-Gordon equation with Kelvin-Voigt damping. One of the interesting features of the equation is that the generator of the associated $C_0$-semigroup has multiple…
Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets…