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

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June 2009, 2(2): 333-343. doi: 10.3934/krm.2009.2.333

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

Gilberto M. Kremer ^1, , Filipe Oliveira ^2, and Ana Jacinta Soares ^2,

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

Received September 2008 Revised February 2009 Published May 2009

Abstract
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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: Chemically reactive gases, Trend to equilibrium, H-Theorem., Boltzmann equation.

Mathematics Subject Classification: Primary: 76P05, 80A32, 82C40; Secondary: 35B3.

Citation: Gilberto M. Kremer, Filipe Oliveira, Ana Jacinta Soares. $\mathcal H$-Theorem and trend to equilibrium of chemically reacting mixtures of gases. Kinetic & Related Models, 2009, 2 (2) : 333-343. doi: 10.3934/krm.2009.2.333

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