Home  About us  Contact
 

Poisson System (poisson + system)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Local existence for the one-dimensional Vlasov,Poisson system with infinite mass

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2007
Stephen Pankavich
Abstract A collisionless plasma is modelled by the Vlasov,Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as ,x, , ,. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behaviour are shown to exist locally in time, and criteria for the continuation of these solutions are established. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Boundary value problem for the N -dimensional time periodic Vlasov,Poisson system

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2006
M. Bostan
Abstract In this work, we study the existence of time periodic weak solution for the N -dimensional Vlasov,Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star-shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Global existence for the Vlasov,Darwin system in ,3 for small initial data

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2003
Saïd Benachour
We prove the global existence of weak solutions to the Vlasov,Darwin system in R3 for small initial data. The Vlasov,Darwin system is an approximation of the Vlasov,Maxwell model which is valid when the characteristic speed of the particles is smaller than the light velocity, but not too small. In contrast to the Vlasov,Maxwell system, the total energy conservation does not provide an L2-bound on the transverse part of the electric field. This difficulty may be overcome by exploiting the underlying elliptic structure of the Darwin equations under a smallness assumption on the initial data. We finally investigate the convergence of the Vlasov,Darwin system towards the Vlasov,Poisson system. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A time-independent approach for computing wave functions of the Schrödinger,Poisson system

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008
C.-S. Chien
Abstract We describe a two-grid finite element discretization scheme for computing wave functions of the Schrödinger,Poisson (SP) system. To begin with, we compute the first k eigenpairs of the Schrödinger,Poisson eigenvalue (ESP) problem on the coarse grid using a continuation algorithm, where the nonlinear Poisson equation is solved iteratively. We use the k eigenpairs obtained on the coarse grid as initial guesses for computing their counterparts of the ESP on the fine grid. The wave functions of the SP system can be easily obtained using the formula of separation of variables. The proposed algorithm has the following advantages. (i) The initial approximate eigenpairs used in the fine grid can be obtained with low computational cost. (ii) It is unnecessary to discretize the partial derivative of the wave function with respect to the time variable in the SP system. (iii) The major computational difficulties such as closely clustered eigenvalues that occur in the SP system can be effectively computed. Numerical results on the ESP and the SP system are reported. In particular, the rate of convergence of the proposed algorithm is O(h4). Copyright © 2007 John Wiley & Sons, Ltd. [source]