Long time asymptotics of a degenerate  linear kinetic transport equation

Tomasz Komorowski

doi:10.3934/krm.2014.7.79

Article Contents

2014, Volume 7, Issue 1: 79-108. Doi: 10.3934/krm.2014.7.79

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Long time asymptotics of a degenerate linear kinetic transport equation

Tomasz Komorowski^1,

1.
IMPAN, ul. Śniadeckich 8, 00-956 Warsaw

Received: December 31, 2012

Revised: May 31, 2013

Published: February 2014

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Abstract

In the present article we prove an algebraic rate of decay towards the equilibrium for the solution of a non-homogeneous, linear kinetic transport equation. The estimate is of the form $C(1+t)^{-a}$ for some $a>0$. The total scattering cross-section $R(k)$ is allowed to degenerate but we assume that $R^{-a}(k)$ is integrable with respect to the invariant measure.

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Mathematics Subject Classification: Primary: 82C40, 82C70; Secondary: 35B40, 82D75.

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