Remarks on entropy and equilibrium states

DOI10.1016/S0893-9659(99)00096-8zbMath0940.35168MaRDI QIDQ1961718

Giuseppe Toscani

Publication date: 19 July 2000

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

entropydensity functionsentropy functional

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (14)

Strong convergence towards self-similarity for one-dimensional dissipative Maxwell models ⋮ Shannon's inequality for the Rényi entropy and an application to the uncertainty principle ⋮ On the ellipsoidal statistical model for polyatomic gases ⋮ Uniqueness for the thin-film equation with a Dirac mass as initial data ⋮ About an H-theorem for systems with non-conservative interactions ⋮ Grad’s equations and hydrodynamics for weakly inelastic granular flows ⋮ Nonlinear diffusion as limit of kinetic equations with relaxation collision kernels ⋮ 1D nonlinear Fokker-Planck equations for fermions and bosons ⋮ Localized minimizers of flat rotating gravitational systems ⋮ Remarks on the \(H\) theorem for a non involutive Boltzmann like kinetic model ⋮ Logarithmic Sobolev inequalities for inhomogeneous Markov Semigroups ⋮ Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics ⋮ Extensive Lyapunov functionals for moment-preserving evolution equations ⋮ Time rescaling and asymptotic behavior of some fourth-order degenerate diffusion equations

Cites Work

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• The Boltzmann equation and its applications
• The mathematical theory of dilute gases
• Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation.
• Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
• A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. I
• The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Entropy is the only increasing functional of Kac's one-dimensional caricature of a Maxwellian gas

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