Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(2): 383-389

Online first article March 3, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b150560

Copyright © The Korean Mathematical Society.

Global stability of the positive equilibrium of a mathematical model for unstirred membrane reactors

Yongli Song and Tonghua Zhang

Hangzhou Normal University, Swinburne University of Technology

Abstract

This paper devotes to the study of a diffusive model for unstirred membrane reactors with maintenance energy subject to a homogeneous Neumann boundary condition. It shows that the unique constant steady state is globally asymptotically stable when it exists. This result further implies the non-existence of the non-uniform steady state solution.

Keywords: diffusion, global stability, local stability, membrane reactor, Lyapunov function

MSC numbers: Primary 35B35, 92D25