Collision of travelling waves in a reaction-diffusion system with global coupling effect. (English) Zbl 0936.35089

Kawaguchi, Satoshi; Mimura, Masayasu

SIAM J. Appl. Math. 59, No. 3, 920-941 (1999).

Authors are concerned with an activator-inhibitor reaction-diffusion system with global coupling effect, which is proposed by Krischer and Mikhailov. By using the interface-dynamics approach, it is shown that when the global coupling inhibition effect is stronger, radially symmetric localized equilibrium solutions are destabilized and there appear travelling wave solutions. When the global coupling effect is sufficiently strong, the collision between two travelling waves is discussed in one and two dimensions.

Reviewer: Georgii Sviridyuk (Chelyabinsk)

MSC:

35K57	Reaction-diffusion equations
35B25	Singular perturbations in context of PDEs
35B32	Bifurcations in context of PDEs

Keywords:

travelling pulse; interface dynamics; activator-inhibitor reaction-diffusion system; radially symmetric localized equilibrium solutions are destabilized