- ANALYSIS OF THE VLASOV-POISSON EQUATION BY USING A VISCOSITY TERM
- Choi, Boo-Yong ; Kang, Sun-Bu ; Lee, Moon-Shik ;
- Journal of the Chungcheong Mathematical Society , volume 26, issue 3, 2013, Pages 501~516
- DOI : 10.14403/jcms.2013.26.3.501

Abstract

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall`s inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.