Document ESAIM: COCV
DOI: 10.1051/cocv:2008033
Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method
Abdoua Tchousso1, 2, Thibaut Besson1 and Cheng-Zhong Xu11 LAGEP, Bâtiment CPE, Université Claude Bernard, Lyon I, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France.
2 Departement de Mathématiques et Informatique, Université Abdou Moumouni de Niamey, BP 10662, Niger; xu@lagep.univ-lyon1.fr
Received November 2, 2005. Revised September 4, 2006 and December 7, 2007. Published online May 30, 2008.
Abstract
In this paper we study asymptotic behaviour of distributed parameter systems governed
by partial differential equations (abbreviated to PDE). We first review some recently developed results
on the stability analysis of PDE systems by Lyapunov's second method. On constructing Lyapunov functionals
we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE
systems. Then we apply the result to establish exponential stability of various chemical engineering
processes and, in particular, exponential stability of heat exchangers. Through concrete examples we
show how Lyapunov's second method may be extended to stability analysis of nonlinear hyperbolic PDE.
Meanwhile we explain how the method is adapted to the framework of Banach spaces Lp,
.
Mathematics Subject Classification. 37L15, 37L45, 93C20
Key words: Hyperbolic symmetric systems, partial differential equations, exponential stability, strongly continuous semigroups, Lyapunov functionals, heat exchangers
© EDP Sciences, SMAI 2008