Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

DOI10.1007/BF00376253zbMath0937.45007OpenAlexW1971953066MaRDI QIDQ1919683

Carlo Cercignani, Reinhard Illner

Publication date: 25 May 2000

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00376253

zbMATH Keywords

global weak solutionnonlinear Boltzmann equationinitial-boundary-value problemcollision kerneldiffusive boundary conditions

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items

Stability estimates of the Boltzmann equation in a half space ⋮ Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation ⋮ Discrete velocity models with general boundary conditions in a slab ⋮ Remarks on a class of kinetic models of granular media: asymptotics and entropy bounds ⋮ Weak solutions of the Boltzmann equation without angle cutoff ⋮ Existence and trend to equilibrium of weak solutions of the boltzmann equation ⋮ Global weak solutions and uniform \(L^p\)-stability of the Boltzmann-Enskog equation ⋮ Strong solutions of the Boltzmann equation in one spatial dimension ⋮ Boundary value problems for the steady Boltzmann equation ⋮ On a Boltzmann equation for Haldane statistics ⋮ Global weak solutions of the Boltzmann equation ⋮ Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions.

Cites Work

• Unnamed Item
• Measure solutions of the steady Boltzmann equation in a slab
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Existence theorems for certain kinetic equations and large data
• A remarkable estimate for the solutions of the Boltzmann equation
• The Boltzmann equation and its applications
• A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal
• The mathematical theory of dilute gases
• Boltzmann asymptotics with diffuse reflection boundary conditions
• Weak solutions of the Boltzmann equation and energy conservation
• Errata: Weak solutions of the Boltzmann equation and energy conservation
• On diffuse reflection at the boundary for the Boltzmann equation and related equations
• Global solutions of Boltzmann's equation and the entropy inequality
• On the StrongL¹Trend to Equilibrium for the Boltzmann Equation