On the Fokker-Planck-Boltzmann equation
DiPerna, R.J.; Lions, Pierre-Louis (1988), On the Fokker-Planck-Boltzmann equation, Communications in Mathematical Physics, 120, 1, p. 1-23. http://dx.doi.org/10.1007/BF01223204
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Mathematical Physics
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Abstract (EN)We consider the Boltzmann equation perturbed by Fokker-Planck type operator. To overcome the lack of strong a priori estimates and to define a meaningful collision operator, we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the Cauchy problem with large data. The proof of stability and existence combines renormalization with an analysis of a defect measure.
Subjects / KeywordsFokker-Planck type operator; Boltzmann equation
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