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

Gilberto M. Kremer; Filipe Oliveira; Ana Jacinta Soares

doi:10.3934/krm.2009.2.333

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2009, Volume 2, Issue 2: 333-343. Doi: 10.3934/krm.2009.2.333

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

1.
Departamento de Física, Universidade Federal do Paraná, Curitiba
2.
Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Lisboa, Portugal; Departamento de Matemática, Universidade do Minho, Braga

Received: September 2008

Revised: February 2009

Published: June 2009

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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.

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Mathematics Subject Classification: Primary: 76P05, 80A32, 82C40; Secondary: 35B35.

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