相关论文: On Morawetz estimates with time-dependent weights …
Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with constant or variable coefficients. We study the distribution $\mu_t$ of the random solution at time $t\in\R$. We assume that the initial probability measure $\mu_0$ has zero…
In this paper we study small amplitude solutions of nonlinear Klein Gordon equations with a potential. Under smoothness and decay assumptions on the potential and a genericity assumption on the nonlinearity, we prove that all small…
We analyze the conclusions of the influence of a Coulomb-type potential on the Klein-Gordon oscillator. We show that the truncation method proposed by the authors do not yield all the eigenvalues of the radial equation but just one of them…
We present a maximal $L_{q}(L_{p})$-regularity theory with Muckenhoupt weights for the equation \begin{equation}\label{eqn 01.26.16:00} \partial^{\alpha}_{t}u(t,x)=a^{ij}(t,x)u_{x^{i}x^{j}}(t,x)+f(t,x),\quad t>0,x\in\mathbb{R}^{d}.…
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…
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 establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schr\"odinger equations. Our results generalize the classical (single-function) Strichartz…
Recently there has been great interest around quantum relativistic models for plasmas. In particular striking advances have been obtained by means of the Klein-Gordon-Maxwell system, which provides a first order approach to the relativistic…
In this article we consider variable coefficient, time-dependent wave equations. Using phase space methods we construct outgoing parametrices and prove Strichartz-type estimates globally in time. This is done in the context of C^2 metrics…
Let $\Delta_\kappa$ be the Dunkl Laplacian on $\mathbb{R}^n$ and $\phi: \mathbb{R}^+ \to \mathbb{R}$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay estimate for a class of dispersive semigroup of the…
We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral (EWI-FP) method for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with a cubic nonlinearity whose strength is characterized by…
It is shown how using the classical Hamilton-Jacobi equation one can arrive at the time-dependent wave equation. Although the former equation was originally used by E.Schroedinger to get the wave equation, we propose a different approach.…
We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
We analyze the d'Alembert equation in the Goedel-type spacetimes with spherical and Lobachevsky sections (with sufficiently rapid rotation). By separating the $t$ and $x_3$ dependence we reduce the problem to a group-theoretical one. In the…
This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are…
The massless Klein--Gordon equation on arbitrary curved backgrounds allows for solutions which develop "tails" inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost sixty years…
In this article one will develop a so-called hyperboloidal foliation method, which is an energy method based on a foliation of space-time into hyperboloidal hypersurfaces. This method permits to treat the wave equations and the Klein-Gordon…
For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by…
Effects of time-dependent applied fields on quantum coupled double-well (DW) systems with Razavy's hyperbolic potential have been studied. By solving the Schr\"{o}dinger equation for the DW system, we have obtained time-dependent occupation…