Related papers: Mathematical aspects of the cold plasma model
The unique existence of a weak solution to the homogeneous closed Dirichlet problem on certain D-star-shaped domains is proven for a mixed elliptic-hyperbolic equation. Equations of this kind arise in models for electromagnetic wave…
A weak Guderley-Morawetz problem is formulated for a mixed elliptic-hyperbolic system that arises in models of wave propagation in cold plasma. Weak solutions are shown to exist in a weighted Hilbert space. This result extends work by…
The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of…
The boundary problem about behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with diffusion boundary conditions is analytically solved. The kinetic equation of Vlasov -…
This paper investigates the existence of weak solutions of biquasilinear boundary value problem for a coupled elliptic-parabolic system of divergence form with discontinuous leading coefficients. The mathematical framework addressed in the…
Energy inequalities are derived for an elliptic-hyperbolic operator arising in plasma physics. These inequalities imply the existence of distribution and weak solutions to various closed boundary-value problems. An existence theorem is…
The propagation and scattering of electromagnetic waves in magnetized plasmas in a state where a global mode has been established or is in turbulence, are of theoretical and experimental interest in thermonuclear fusion research.…
Electromagnetic wave propagation through cold collision free plasma is studied using the nonlinear perturbation method. It is found that the equations can be reduced to the modified Kortweg-de Vries equation.
This work presents a multidisciplinary mathematical model, as a set of coupled governing equations and auxiliary relations describing the fluid-flow, thermal, and electric fields of partially-ionized plasma with low magnetic Reynolds…
This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
In this short note, we present some work on investigating electron temperatures and potentials in steady or unsteady dilute plasma flows. The analysis is based on the detailed fluid model for electrons. Ionization, normalized electron…
A solution of the Riemann problem is constructed for a nonstrictly hyperbolic inhomogeneous system of equations describing one-dimensional cold plasma oscillations. Each oscillation period includes one rarefaction wave and one shock wave…
The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…
A detailed simple model is applied to study a high temperature plasma ball. It is assumed that the ions and delocalized electrons are distributed randomly throughout the charged plasma ball (extra/missing charge is assumed to be found in a…
We study a 1D geometry of a plasma confined between two conducting floating walls with applications to laboratory plasmas. These plasmas are characterized by a quasi-neutral bulk that is joined to the wall by a thin boundary layer called…
We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy…
Simulation results are presented to demonstrate electron temperature and electrical potential development in dilute and cold plasma development. The simulation method is a hybrid method which adopted fluid model for electrons due to their…
The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For some simplified formulation of the problem, a criterion for the…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…