This paper is devoted to model (1) for escherichia coli, introduced in [1]. Based on the experimental observations of Budrene and Berg [2, 3], Tyson and coworkers derived (1) with n cell density, c chemotrattactant concentration and s stimulant concentration. Our aim is to study the stability of constant meaning full solution and ultimately boundedness of the solutions. Precisely: (i) linear and nonlinear stability is proved by using a peculiar Lyapunov function, (ii) the ultimately boundedness of the solutions in the L2-norm is obtained, (iii) conditions guaranteeing the global stability are also obtained.
Stability and absorbing set of parabolic chemotaxis model of Escherichia coli / Rionero, S.; Vitiello, Maria. - In: NONLINEAR ANALYSIS. - ISSN 1392-5113. - 18:2(2013), pp. 210-226.
Stability and absorbing set of parabolic chemotaxis model of Escherichia coli
VITIELLO, Maria
2013-01-01
Abstract
This paper is devoted to model (1) for escherichia coli, introduced in [1]. Based on the experimental observations of Budrene and Berg [2, 3], Tyson and coworkers derived (1) with n cell density, c chemotrattactant concentration and s stimulant concentration. Our aim is to study the stability of constant meaning full solution and ultimately boundedness of the solutions. Precisely: (i) linear and nonlinear stability is proved by using a peculiar Lyapunov function, (ii) the ultimately boundedness of the solutions in the L2-norm is obtained, (iii) conditions guaranteeing the global stability are also obtained.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
