Stability of solutions of chemotaxis equations in reinforced random walks

By A. Friedman, J. Tello. 2002

94 citations recorded by the source corpus.

In this paper we consider a nonlinear system of differential equations consisting of one parabolic equation and one ordinary differential equation. The system arises in chemotaxis, a process whereby living organisms respond to chemical substance by moving toward higher, or lower, concentrations of the chemical substance, or by aggregating or dispersing. We prove that stationary solutions of the system are asymptotically stable.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/9027d8c63b6f7f9f13ec27471abdb7d1a265a9e6

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In Computational Theory and Mathematics

In Modeling and Simulation

In Molecular Biology

Citations in the corpus

Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions (2004, background): “Finally we would like to cite [20], where the authors consider for the evolution of c an ODE of the type ∂c ∂t = g(c, n) under some hypotheses on g not satisfied in the case we consider in system (4).”
Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant (2015, methodology): “[19] M. Negreanu, J.I. Tello, On a comparison method to reaction-diffusion systems and its applications to chemotaxis, Discrete Contin.”
A Chemotaxis System with Logistic Source (2007, methodology): “The proof generalizes some ideas originally used in Tello and Chaplain (preprint) for g as given by (5.2) (see also Friedman and Tello, 2002; Tello, 2004).”