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

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.


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