Zeitschrift für Analysis und ihre Anwendungen
Vol. 19, No. 1, pp. 77-93 (2000)
Exponential Stability of a Nonlinear Distributed Parameter System
J. Tervo and M. NihtiläDept. Appl. Math. Univ., POB 1627, FIN-70211 Kuopio Dept. Food Techn. Univ., POB 27 (Viikki), FIN-00014 University of Helsinki
Abstract: A nonlinear parabolic partial differential equation model describing the behaviour of a distributed parameter fixed-bed bioreactor is studied here. Exponential stability around the steady state solution for exponentially decaying deviations in the input and disturbance are proved via abstract formulation of the model as an evolution equation and by utilizing semigroup theory and asymptotic stability of the corresponding evolution operator.
Keywords: infinite-dimensional nonlinear systems, parabolic partial differential equations, exponential stability, fixed-bed bioreactors
Classification (MSC2000): 93C20, 93C80 35K57
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Electronic fulltext finalized on: 25 Jul 2001. This page was last modified: 9 Nov 2001.