Affiliations: Max‐Planck‐Institute for Mathematics in the Sciences, Inselstr. 22‐26, D‐04103 Leipzig, Germany E‐mail: dkhil@mis.mpg.de | Département de Mathématiques, Université de Cergy‐Pontoise, 2, avenue A. Chauvin, 95302 Cergy‐Pontoise cedex, France | Laboratory of Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, N12 W6 Sapporo, 060‐0812, Japan
Note: [] Supported by RTN program: Fronts‐Singularities, RTN contract HPRN‐CT‐2002‐00274. This work was done while the author was at the Département de Mathématiques, Université de Cergy‐Pontoise, 2, avenue A. Chauvin, 95302 Cergy‐Pontoise cedex, France.
Note: [] Corresponding author.
Abstract: We consider the Gray–Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to exist near the equal diffusivities and equal transformation rates case. We also provide numerical simulations illustrating our results.
