Stability and absorbing set of parabolic chemotaxis model of Escherichia coli - Rionero, Salvatore; Vitiello, Maria (Nonlinear Analysis: Modelling and Control, 2013)
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.
Keywords: chemotaxis model; linear and nonlinear stability; absorbing set