The Enskog-Boltzmann equation in the whole space \({\mathbb{R}}^ 3:\) Some global existence, uniqueness and stability results

DOI10.1016/0898-1221(87)90168-4zbMath0633.35072OpenAlexW2038710375MaRDI QIDQ1096092

Giuseppe Toscani, Nicola Bellomo

Publication date: 1987

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(87)90168-4

zbMATH Keywords

uniquenessasymptotic stabilitywell-posednessglobal existenceinitial datarate of decayEnskog-Boltzmann equationhigh gas densitiesinitial- value problem

Mathematics Subject Classification ID

Related Items (17)

On uniqueness and stability for the Boltzmann-Enskog equation ⋮ Uniform stability of the solutions to the relativistic Enskog equation ⋮ Global existence in \(L^ 1\) for the modified nonlinear Enskog equation in \({\mathbb{R}}^ 3\) ⋮ Global existence for the relativistic Enskog equations ⋮ New estimations of the nonlinear Boltzmann operator and their application to existence theorems ⋮ The Enskog process ⋮ Global well-posedness of a binary-ternary Boltzmann equation ⋮ On the asymptotic equivalence between the Enskog and the Boltzmann equations. ⋮ Global existence in \(L^ 1\) for the generalized Enskog equation. ⋮ On the modified Enskog equation for elastic and inelastic collisions. Models with spin ⋮ Global weak solutions and uniform \(L^p\)-stability of the Boltzmann-Enskog equation ⋮ Invisible Control of Self-Organizing Agents Leaving Unknown Environments ⋮ New properties of a class of generalized kinetic equations ⋮ The Enskog process for hard and soft potentials ⋮ Stability of global solution for the relativistic Enskog equation near vacuum ⋮ On the inelastic Enskog equation near vacuum ⋮ The inelastic Enskog equation with external force

Cites Work

• Local solutions to the initial and initial boundary value problem for the Boltzmann equation with an external force. I
• The Boltzmann equation: global existence for a rare gas in an infinite vacuum
• The Boltzmann equation. I. Uniqueness and local existence
• Global existence and asymptotic behavior for the discrete velocity models of the Boltzmann equation
• On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability
• Irreversibility in Heisenberg Spin Systems. II. Approximate Solution of the High-Temperature Kinetic Equations
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