TY - JOUR

T1 - Long time asymptotics of a system for plasma diffusion

AU - Rosenau, Philip

AU - Turkel, Eli

N1 - Funding Information:
Research was partially supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-17070 while the second author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665.

PY - 1987/3/1

Y1 - 1987/3/1

N2 - We analyze a system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field. We demonstrate that the solution to this system tends to a time asymptotic state which is of space-time separable form, ϕ(t)f(x). Furthermore, f(x) is independent of the initial conditions and ϕ(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects as radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

AB - We analyze a system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field. We demonstrate that the solution to this system tends to a time asymptotic state which is of space-time separable form, ϕ(t)f(x). Furthermore, f(x) is independent of the initial conditions and ϕ(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects as radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

UR - http://www.scopus.com/inward/record.url?scp=15544364815&partnerID=8YFLogxK

U2 - 10.1080/00411458708204671

DO - 10.1080/00411458708204671

M3 - מאמר

AN - SCOPUS:15544364815

VL - 16

SP - 377

EP - 391

JO - Journal of Computational and Theoretical Transport

JF - Journal of Computational and Theoretical Transport

SN - 2332-4309

IS - 2-3

ER -