Rui Peng et al 2008 Nonlinearity 21 1471 doi:10.1088/0951-7715/21/7/006
Rui Peng1,5, Junping Shi2,3 and Mingxin Wang4
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Understanding of spatial and temporal behaviour of interacting species or reactants in ecological or chemical systems has become a central issue, and rigorously determining the formation of patterns in models from various mechanisms is of particular interest to applied mathematicians. In this paper, we study a bimolecular autocatalytic reaction–diffusion model with saturation law and are mainly concerned with the corresponding steady-state problem subject to the homogeneous Neumann boundary condition. In particular, we derive some results for the existence and non-existence of non-constant stationary solutions when the diffusion rate of a certain reactant is large or small. The existence of non-constant stationary solutions implies the possibility of pattern formation in this system. Our theoretical analysis shows that the diffusion rate of this reactant and the size of the reactor play decisive roles in leading to the formation of stationary patterns.
82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces
87.23.Cc Population dynamics and ecological pattern formation
Surfaces, interfaces and thin films
Issue 7 (July 2008)
Received 27 September 2007, in final form 18 March 2008
Published 21 May 2008
Rui Peng et al 2008 Nonlinearity 21 1471
B R Chakraborty et al 2005 Nanotechnology 16 1006
K Kuroda et al 2002 Class. Quantum Grav. 19 1237
Anthony Dyson et al 2000 Meas. Sci. Technol. 11 554
Roberto Iengo et al JHEP11(2009)020
N B Tufillaro 1990 Eur. J. Phys. 11 122
C B Suarez 1970 J. Phys. B: At. Mol. Phys. 3 1389
W Bich 2003 Metrologia 40 306
K B Joshi and U Paliwal 2009 Phys. Scr. 80 055601
Daniel C Cabra et al 1997 J. Phys. A: Math. Gen. 30 2699