相关论文: On Classical Solutions of the Relativistic Vlasov-…
We are concerned with wave equations associated to some Liouville-type problems on compact surfaces, focusing on sinh-Gordon equation and general Toda systems. Our aim is on one side to develop the analysis for wave equations associated to…
The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys…
We are concerned with the Sinh-Gordon equation in bounded domains. We construct blow up solutions with residual mass exhibiting either partial or asymmetric blow up, i.e. where both the positive and negative part of the solution blow up.…
In this article it is shown that the fundamental equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of curved space-time. We further generalize the results to…
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…
It is well known that for the quasilinear Klein-Gordon equation with quadratic nonlinearity and sufficiently decaying small initial data, there exists a global smooth solution if the space dimensions $d\geq2$. When the initial data are of…
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…
The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a ''particle'', which is both passively affected by, and actively affecting, a diffusion process of its…
It is well-known that the solution of the classical linear wave equation with compactly supported initial condition and vanishing initial velocity is also compactly supported in a set depending on time : the support of the solution at time…
In this paper we consider the Klein-Gordon equation on spherically symmetric background spacetimes with a constant area radius. The spacetimes under consideration are Nariai and Pleba\'nski-Hacyan, and can be considered constant radius…
While much literature on chemotaxis systems focuses on bounded domains, this paper emphasizes the global existence of classical solutions for three primary chemotaxis systems with a logistic source on $\mathbb{R}^n$. We present a unified…
The classical two-dimensional one-component plasma is an exactly solvable model, at some special temperature, even when the one-body potential acting on the particles has a quadrupolar term. As a supplement to a recent work of Di Francesco,…
It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of such solutions after gradient blow-up. This continuation is…
The Klein-Gordon equation is solved for di-Holeums (gravitational bound states of two micro black holes) for scalar and vector gravity in its static limit. The relativistic models confirm the predictions of the nonrelativistic Newtonian…
This paper is devoted to the study of relativistic Vlasov-Maxwell system in three space dimension. For a class of large initial data, we prove the global existence of classical solution with sharp decay estimate. The initial Maxwell field…
In this paper we will see that the global or local existence of solutions to \begin{eqnarray*} \dfrac{\partial u_{1}}{\partial t} & = & \mathit{k}_{1} (t) \Delta u_{1} + h_{1}(t) u_{1}^{p_{11}} u_{2}^{p_{12}},\\ \dfrac{\partial…
This paper is devoted to the study of the dynamics of charged particles in a weakly inhomogeneous dilute gas. More precisely, we consider the existence of unique global in time classical solutions for the Vlasov-MaxwellBoltzmann system and…
Two alternative ways of description an evolution constrained by mass-shell equation are given by the hyperbolic and the periodic angles. In the both cases the angles are proportional to the mass. The differential operators with respect to…
The motion of a collisionless plasma is described by the Vlasov-Poisson system, or in the presence of large velocities, the relativistic Vlasov-Poisson system. Both systems are considered in one space and one momentum dimension, with two…
We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the orders of…