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IMA Journal of Mathematical Control and Information Advance Access published online on June 30, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl013
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received September 9, 2005
Revised February 21, 2006
Accepted March 13, 2006

Article

Asymptotic behaviour of state trajectories for a class of tubular reactor non-linear models

B. Aylaj 1, M. E. Achhab 1, and M. Laabissi 1 *

1 Laboratoire d'Ingénierie Mathématique (LINMA), Département de Mathématique et Informatique, Faculté des Sciences, BP 20, El Jadida, Morocco

* To whom correspondence should be addressed.
M. Laabissi, E-mail: laabissi{at}ucd.ac.ma


  Abstract

We prove the global existence of the state trajectories for a class of non-linear systems arising from convection-dispersion-reaction processes. It is also shown that there is at least one steady state in the set of physically feasible states for such systems. The uniqueness and the stability analysis of this steady-state solution are discussed. Our approach is based on the analysis of a non-linear set of partial differential equations, using the upper and lower solutions, dissipativity properties, a subtangential condition and the positivity of the related C0-semigroup.

Keywords: tubular reactor; non-linear distributed parameter systems; equilibrium profile; positive C0-semigroup; compact semigroup; dissipativity.
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