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  • 1
    Electronic Resource
    Electronic Resource
    On the initial value problem for the Vlasov-Poisson-Fokker-Planck system with initial data in Lp spaces (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 825-839 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper the global existence of weak solutions for the Vlasov-Poisson-Fokker-Planck equations in three dimensions is proved with an L1 ∩ Lp initial data. Also, the global existence of weak solutions in four dimensions with small initial data is studied. A convergence of the solutions is obtained to those built by E. Horst and R. Hunze when the Fokker-Planck term vanishes. In order to obtain the a priori necessary estimates a sequence of approximate problems is introduced. This sequence is obtained starting from a non-linear regulation of the problem together with a linearization via a time retarded mollification of the non-linear term. The a priori bounds are reached by means of the control of the kinetic energy in the approximate sequence of problems. Then, the proof is completed obtaining the equicontinuity properties which allow to pass to the limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670181006
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Global weak solutions for the initial-boundary-value problems Vlasov-Poisson-Fokker-Planck System (1998)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 21 (1998), S. 907-938 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work is devoted to prove the existence of weak solutions of the kinetic Vlasov-Poisson-Fokker-Planck system in bounded domains for attractive or repulsive forces. Absorbing and reflection-type boundary conditions are considered for the kinetic equation and zero values for the potential on the boundary. The existence of weak solutions is proved for bounded and integrable initial and boundary data with finite energy. The main difficulty of this problem is to obtain an existence theory for the linear equation. This fact is analysed using a variational technique and the theory of elliptic-parabolic equations of second order. The proof of existence for the initial-boundary value problems is carried out following a procedure of regularization and linearization of the problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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