Three-dimensional waves in excitable reaction-diffusion systems (Q1104259)

The authors deal with the reaction-diffusion system \[ \epsilon u_ t=\epsilon^ 2\Delta u+F(u,w),\quad \epsilon w_ t=G(u,w),\quad in\quad M,\quad t>0, \] where \(u\in {\mathbb{R}}^ 1 \)and \(w\in {\mathbb{R}}^ m,\) \(0<\epsilon <<1\), M being a closed orientable surface imbedded in \({\mathbb{R}}^ 3.\) They then investigate the existence and propagation of rotationally symmetric and double spiral waves on the sphere and on the torus [see also the paper of the same authors reviewed above, Zbl 0646.92001].