A kinetic reaction model: Decay to equilibrium and macroscopic limit

Lukas  Neumann; Christian  Schmeiser

doi:10.3934/krm.2016007

Article Contents

2016, Volume 9, Issue 3: 571-585. Doi: 10.3934/krm.2016007

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A kinetic reaction model: Decay to equilibrium and macroscopic limit

Lukas Neumann^1, and
Christian Schmeiser^2,

1.
Universität Innsbruck, Technikerstraße 13, 6020 Innsbruck
2.
Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien

Received: March 2015

Revised: September 2015

Published: September 2016

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Abstract

We propose a kinetic relaxation-model to describe a generation-recombination reaction of two species. The decay to equilibrium is studied by two recent methods [9,13] for proving hypocoercivity of the linearized equations. Exponential decay of small perturbations can be shown for the full nonlinear problem. The macroscopic/fast-reaction limit is derived rigorously employing entropy decay, resulting in a nonlinear diffusion equation for the difference of the position densities.

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Mathematics Subject Classification: Primary: 76P05; Secondary: 82B40, 82C40, 82D05, 76V05.

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