Travelling wavefronts of Belousov–Zhabotinskii system with diffusion and delay

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
Applied Mathematics Letters (Impact Factor: 1.48). 03/2009; 22(3):341-346. DOI: 10.1016/j.aml.2008.04.006
Source: DBLP

ABSTRACT This paper is concerned with the existence, nonexistence and minimal wave speed of the travelling wavefronts of Belousov–Zhabotinskii system with diffusion and delay.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Following J.D. Murray, we consider a system of two differential equations that models traveling fronts in the Noyes-Field theory of the Belousov-Zhabotinsky (BZ) chemical reaction. We are also interested in the situation when the system incorporates a delay $h\geq 0$. As we show, the BZ system has a dual character: it is monostable when its key parameter $r \in (0,1]$ and it is bistable when $r >1$. For $h=0, r\not=1$, and for each admissible wave speed, we prove the uniqueness of monotone wavefronts. Next, a concept of regular super-solutions is introduced as a main tool for generating new comparison solutions for the BZ system. This allows to improve all previously known upper estimations for the minimal speed of propagation in the BZ system, independently whether it is monostable, bistable, delayed or not. Special attention is given to the critical case $r=1$ which to some extent resembles to the Zeldovich equation.
    Journal of Differential Equations 03/2011; 254(9). DOI:10.1016/j.jde.2013.02.005 · 1.57 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper is concerned with a reaction–diffusion equation with time delay, which describes the dynamics of the blood cell production. The existence of the traveling wavefront is given by using the upper–lower solution technique and the monotone iteration.
    Applied Mathematics Letters 04/2010; 23(4-23):426-431. DOI:10.1016/j.aml.2009.11.011 · 1.48 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Existence of travelling wave front solution is established for diffusive and competitive Lotka–Volterra system with delays. The approach used in this paper is the upper-lower solution technique and the monotone iteration. The same results are suitable to Belousov–Zhabotinskii model with delays and cooperative Lotka–Volterra system with delays.
    Nonlinear Analysis Real World Applications 06/2010; 11(3):1323-1329. DOI:10.1016/j.nonrwa.2009.02.020 · 2.34 Impact Factor


1 Download
Available from