Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
21 (1998), S. 985-1014
ISSN:
0170-4214
Keywords:
Vlasov-Poisson-Fokker-Planck
;
long-time behaviour
;
fundamental solutions
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We study the long-time behaviour of solutions of the Vlasov-Poisson-Fokker-Planck equation for initial data small enough and satisfying some suitable integrability conditions. Our analysis relies on the study of the linearized problems with bounded potentials decaying fast enough for large times. We obtain global bounds in time for the fundamental solutions of such problems and their derivatives. This allows to get sharp bounds for the decay of the difference between the solutions of the Vlasov-Poisson-Fokker-Planck equation and the solution of the free equation with the same initial data. Thanks to these bounds, we get an explicit form for the second term in the asymptotic expansion of the solutions for large times. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
Type of Medium:
Electronic Resource
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