Time asymptotic behaviour for Rotenberg's model with Maxwellboundary conditions

Khalid Latrach; Hatem Megdiche

doi:10.3934/dcds.2011.29.305

Article Contents

2011, Volume 29, Issue 1: 305-321. Doi: 10.3934/dcds.2011.29.305

This issue Previous Article Non-integrability of the collinear three-body problem Next Article Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups

Time asymptotic behaviour for Rotenberg's model with Maxwell boundary conditions

Khalid Latrach^1, and
Hatem Megdiche^2,

1.
Clermont Université, Université Blaise Pascal, Laboratoire de Matématiques, BP. 10448, F-63000 CLERMONT-FERRAND, CNRS, UMR 6620, Laboratoire de Mathématiques, F-63177 AUBIERE
2.
Département de Mathématiques, Faculté des Sciences de GABÈS, Cité Erriadh 6072, Zrig, GABÈS

Received: July 2009

Revised: May 2010

Published: January 2011

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we discuss the large time behavior of the solution to the Cauchy problem governed by a transport equation with Maxwell boundary conditions arising in growing cell population in $L^1$-spaces. Our result completes previous ones established in [3] in $L^p$-spaces with $1 < p < \infty$.

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Mathematics Subject Classification: 47G20, 47D06, 47A55.

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