$L^1$-continuous dependence of mild solutions to the Fokker-Planck-Boltzmann equation
by Seung-Yeal Ha   Ho Lee   Se Eun Noh  

Vol. 2 No. 4 (2007) P.893~P.905

ABSTRACT

We present a uniform $L^1$-stability estimate for mild solutions to the Fokker-Planck-Boltzmann equation. For stability estimate, we derive a Gronwall type estimate using dispersion estimates for mild solutions due to the hypoelliptic structure of the Vlasov-Fokker-Planck operator.

KEYWORDS
$L^1$-stability, Fokker-Planck-Boltzmann equation, dissipative kinetic system

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35L60

MILESTONES

Received: 2007-07-17
Revised :
Accepted:

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