$\mathcal H$-Theorem and trend to equilibrium of chemically reacting mixtures of gases

Pages: 333 - 343, Volume 2, Issue 2, June 2009

doi:10.3934/krm.2009.2.333       Abstract        Full Text (184.0K)

Gilberto M. Kremer - Departamento de Física, Universidade Federal do Paraná, Curitiba, Brazil (email)
Filipe Oliveira - Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Lisboa, Portugal; Departamento de Matemática, Universidade do Minho, Braga, Portugal (email)
Ana Jacinta Soares - Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Lisboa, Portugal; Departamento de Matemática, Universidade do Minho, Braga, Portugal (email)

Abstract: The trend to equilibrium of a quaternary mixture of monatomic gases undergoing a reversible reaction of bimolecular type is studied in a quite rigorous mathematical picture within the framework of Boltzmann equation extended to chemically reacting mixtures of gases. The $\mathcal H$-theorem and entropy inequality allow to prove two main results under the assumption of uniformly boundedness and equicontinuity of the distribution functions. One of the results establishes the tendency of a reacting mixture to evolve to an equilibrium state as time becomes large. The other states that the solution of the Boltzmann equation for chemically reacting mixtures of gases converges in strong $L^1$-sense to its equilibrium solution.

Keywords:  Boltzmann equation, Chemically reactive gases, Trend to equilibrium, H-Theorem.
Mathematics Subject Classification:  Primary: 76P05, 80A32, 82C40; Secondary: 35B35.

Received: September 2008;      Revised: February 2009;      Published: May 2009.