Applied Mathematics Letters 22 (2009) 341–346
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Applied Mathematics Letters
journal homepage: www.elsevier.com/locate/aml
Travelling wavefronts of Belousov–Zhabotinskii system with diffusion
Guo Lin∗, Wan-Tong Li
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
a r t i c l e i n f o
Received 17 January 2007
Received in revised form 1 April 2008
Accepted 25 April 2008
Minimal wave speed
a b s t r a c t
This paper is concerned with the existence, nonexistence and minimal wave speed of the
travelling wavefronts of Belousov–Zhabotinskii system with diffusion and delay.
© 2008 Elsevier Ltd. All rights reserved.
In 1959, Belousov  proposed the so-called Belousov–Zhabotinskii system to model the chemical reaction, and one of
its simplified models takes the form as follows
and bromide ion, respectively, ∆ is the Laplacian operator on R. Model (1.1), in fact, was also derived in biochemical and
biological fields, see [10,11,21,22]. Recalling the chemical and biological backgrounds of (1.1), the following asymptotical
boundary conditions were proposed [5,6,17,20]
= ∆U(x,t) + U(x,t)[1 − U(x,t) − rV(x,t)],
= ∆V(x,t) − bU(x,t)V(x,t),
where x ∈ R,t > 0,r ∈ (0,1),b is a positive constant, and U,V ∈ R correspond to the concentration of bromic acid
x→−∞U(x,t) = 0,
x→∞U(x,t) = 1,
On the dynamics of (1.1) and (1.2), travelling wavefront, which takes the form of(U(x,t),V(x,t)) = (ρ(x+ct),?(x+ct))
for some wave speed c > 0 and monotone wave profile function (ρ,?), attracted much attention, see Murray ,
Troy , Ye and Wang  and the references cited therein. Moreover, from the viewpoint of the chemical reaction, the
travelling wavefronts of (1.1) and (1.2) have significant sense, namely, the waves move from a region of higher bromic
x→−∞V(x,t) = 1,
x→∞V(x,t) = 0.
$Supported by NSFC (No. 10571078), NSF of Gansu Province of China (No. 3ZS061-A25-001).
E-mail address: firstname.lastname@example.org (G. Lin).
0893-9659/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.
G. Lin, W.-T. Li / Applied Mathematics Letters 22 (2009) 341–346
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