@misc{DellnitzGolubitskyHohmannetal., author = {Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, title = {Spirals in Scalar Reaction-Diffusion Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1720}, number = {SC-95-06}, abstract = {Spiral-like patterns are an often observed phenomenon in chemical experiments such as the Belousov-Zhabotinskii reaction. The talk is concerned with a new PDE model whose solutions have the form of rotating spirals. In contrast to previous approaches it is based on a {\em scalar\/} reaction diffusion equation defined on a disk. A particular choice of boundary conditions leads to a non-selfadjoint operator which permits non-trivial dynamics. We study this equation using a combination of equivariant bifurcation theory and numerical simulations. The latter involves the direct simulation of the time dependent system as well as the computation of rotating waves and their stability.}, language = {en} }