GLOBAL BIFURCATION OF WAVES

In this note it will be shown how a theorem of Alexander [1] and Ize [9] together with computational results of Alexander and Yorke [4] and Alexander and Fitzpatrick [2] may be used to generalize the existence theorem for, and to prove some global results about, certain wave-like solutions of nonlinear systems of partial differential equations. The equations to be studied are weakly coupled parabolic systems of equations defined on a bounded axisymmetric domain. Such equations are often called reaction-diffusion equations (or interaction-diffusion equations) and arise in many parts of biology and chemistry. The question as to how wave-like solutions of these equations may bifurcate from a family of trivial solutions was studied by Auchmuty [5] and the results will be considerably extended here. © 1979 Springer-Verlag.