Related papers: Mathematical aspects of the cold plasma model
In his deep and prolific investigations of heat diffusion, Lam\'e was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular he derived explicit results for the…
The analytical solution of the boundary problem on behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in a slab of the conducting medium is received. The kinetic Vlasov---Boltzmann…
In terms of initial data, a sufficient condition for the smoothness of the solution to the Cauchy problem for one-dimensional relativistic cold plasma equations over any given time interval is found. Unlike the non-relativistic case, such…
The electromagnetic instabilities excited by the temperature anisotropy have been always one of the interesting issues in real high-density physical systems, where the relativistic and quantum effects due to spin can be important. This…
We study a one-dimensional system of cold plasma equations taking into account electron-ion collisions in both relativistic and nonrelativistic cases. It is known that for a constant collision coefficient $\nu$, the solution to the Cauchy…
This article studies, both theoretically and numerically, a nonlinear drift-diffusion equation describing a gas of fermions in the zero-temperature limit. The equation is considered on a bounded domain whose boundary is divided into an…
Electrostatic oscillations in cold electron-positron plasmas can be coupled to a propagating electromagnetic mode if the background magnetic field is inhomogeneous. Previous work considered this coupling in the quasi-linear regime,…
We consider the Riemann problem for relativistic flows of polytropic fluids and find relations for the flow characteristics. Evolution of physical quantities take especially simple form for the case of cold magnetized plasmas. We find…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
The effects of radiation on the structure of shocks in a fully-ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity…
We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability…
We study the distribution of the mean radial displacement of charges of a 2D one-component plasma in the thermodynamic limit $N\to\infty$ at finite temperature $\beta>0$. We compute explicitly the large deviation functions showing the…
A simple model is applied to study a high temperature rather dense plasma ball. It is assumed that the ions and delocalized electrons are distributed uniformly throughout the ball, and extra/missing charge is found in a thin layer on the…
We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases explicit formulas for solution are given like layer potentials…
We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It occurs specifically in the heat-mass transfer theory. We…
To analyze nonidealities inherent to degenerate plasma, a quantum collective approach is developed. Thermodynamic functions of a system of partially degenerate electrons and strongly coupled ions are derived from first principles. The model…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
A procedure that allows study of unstable stability of a boundary layer between plasma and a magnetic field has been developed. Layer equilibrium for one reason or another is not set but follows from strict solution of kinetic equation with…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
A dispersion relation for electromagnetic wave propagation in a strongly magnetized cold plasma is deduced, taking photon-photon scattering into account. It is shown that the combined plasma and quantum electrodynamic effect is important…