On long time asymptotics of the Vlasov-Poisson-Boltzmann equation

Journal Article · Mon Dec 31 23:00:00 EST 1990 · Communications in Partial Differential Equations; (United States)

DOI:https://doi.org/10.1080/03605309108820765· OSTI ID:5354948

Desvillettes, L ^[1]; Dolbeault, J ^[2]

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1. Ecole Normale Superieure, Paris (France)
2. Univ. Paris IX-Dauphine (France)

The authors prove in this work the convergence towards equilibrium for a regular solution of the Vlasov-Poisson-Boltzmann equation in a bounded domain with appropriate boundary conditions. Note that such a result is already known for the Boltzmann equation, even for renormalized solutions (Cf(A) and (De)). Moreover, they give a description of the Maxwellian steady states for such a plasma, when the mass and energy of the particles are fixed. Note that D.Gogny and P-L.Lions have already given such a description when the mass and temperature are fixed (Cf(G,L)). In section 2, they prove that in the long time asymptotics, the density of particles satisfying the Vlasov-Poisson-Boltzmann equation converges to a Maxwellian with zero bulk velocity, and uniform temperature. Moreover, they give an equation for the electric potential in this limit.

• OSTI ID: 5354948
• Journal Information: Communications in Partial Differential Equations; (United States), Journal Name: Communications in Partial Differential Equations; (United States) Vol. 16:2-3; ISSN 0360-5302; ISSN CPDID
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
COLLISIONS
CONVERGENCE
DENSITY
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
ELECTRIC POTENTIAL
EQUATIONS
KERNELS
KINETIC EQUATIONS
MEAN-FIELD THEORY
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PLASMA
POISSON EQUATION
SCATTERING