Parabolic limit and stability of the Vlasov-Fokker-Planck system. (English) Zbl 1018.76048
Summary: We analyze the stability of Vlasov-Poisson-Fokker-Planck system with respect to the variation of its constant parameters, scaled thermal velocity and scaled thermal mean free path. For the case in which the scaled thermal velocity is the inverse of the scaled thermal mean free path and the latter tends to zero, a parabolic limit equation is obtained for the mass density. Depending on the space dimension and on the hypothesis on initial data, the convergence result in \(L^1\) is weak and global in time or strong and local in time.
MSC:
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
Keywords:
stability; Vlasov-Poisson-Fokker-Planck system; scaled thermal velocity; scaled thermal mean free path; parabolic limit equation; convergenceReferences:
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