相关论文: Evolution of Observables in a Numerical Kinetic Mo…

As is well known from the work of R. Glassey} and J. Schaeffer, the main energy estimates which are used in global existence results for the gravitational Vlasov-Poisson system do not apply to the relativistic version of this system, and…

Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes,…

Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of…

We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal…

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…

We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a nonlocal equation of state. This equation relates, at a given point, the components of the corresponding…

We study the long-time behavior of symmetric solutions of the nonlinear Boltzmann equation and a closely related nonlinear Fokker-Planck equation. If the symmetry of the solutions corresponds to shear flows, the existence of stationary…

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter $c>c_0$ for a properly large and positive $c_0$. A local existence…

We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded…

It is shown that the Lattice Boltzmann equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.

A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…

For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for…

In this paper we provide approximate analytical analysis of stability of nonsingular inflationary chaotic-type cosmological models. Initial conditions for nonsingular solutions at the bounce correspond to dominance of potential part of the…

Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…

A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…

We develop error estimates for the semi-discrete conservative spectral method for the approximation of the elastic and inelastic space homogeneous Boltzmann equation introduced by the authors in \cite{GT09}. In addition we study the long…

A class of general relativistic solutions in isotropic spherical polar coordinates are discussed which describe compact stars in hydrostatic equilibrium. The stellar models obtained here are characterized by four parameters, namely,…

Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…

In this paper we develop high-order asymptotic-preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi, where asymptotic preserving exponential Runge-Kutta methods for the…

We numerically analyse solutions of the spherically symmetric gravitational Vlasov-Poisson system close to compactly supported stable steady states. We observe either partially undamped oscillations or macroscopically damped solutions. We…