zbMATH — the first resource for mathematics

A trace theorem in kinetic theory. (English) Zbl 0744.45005
Summary: A mathematical assumption made in a recent paper by the second author [Arch. Ration. Mech. Anal. 116, No. 4, 307-315 (1991)] on the traces of the solutions of initial-boundary value problems for the Boltzmann equation is shown here to be true in the case of a domain whose boundary is a Lyapunov surface with purely diffusing boundary conditions.

45K05 Integro-partial differential equations
82B40 Kinetic theory of gases in equilibrium statistical mechanics
Full Text: DOI
[1] Hamdache, K., Initial-boundary value problem for boltzman equation. global existence of weak solutions, Arch. rat. mech. anal., (1991), (to appear)
[2] DiPerna, R.; Lions, P.L., On the Cauchy problem for Boltzmann equations, Ann. of math., 130, 2, 321-366, (1989) · Zbl 0698.45010
[3] Cercignani, C., On the initial-boundary value problem for the Boltzmann equation, Arch. rat. mech. anal, (1991), (to appear) · Zbl 0753.76151
[4] Ukai, S., Solutions of the Boltzmann equation, Pattern and waves-qualitative analysis of nonlinear differential equations, 37-96, (1986)
[5] Cercignani, C., Mathematical methods in kinetic theory, (1990), Plenum Press New York · Zbl 0726.76083
[6] Mikhlin, S.G., Linear integral equations, (1960), Hindustan Publishing Corp Delhi · Zbl 0142.39201
[7] Zabreyko, P.P., Integral equations—A reference text, (1975), Noordhoff International Publishing Leyden
[8] Riesz, F.; Sz.-Nagy, B., Leçons d’analyse fonctionelle, (1953), Académie des Sciences de Hongrie · Zbl 0051.08403
[9] Maslova, N.B., The solvability of stationary problems for Boltzmann’s equation at large Knudsen numbers, U.S.S.R. comput. maths. math. phys., 17, 4, 194-204, (1978) · Zbl 0383.35063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.