A reaction-diffusion system of (lambda)–(omega) type Part I: Mathematical analysis

We study two coupled reaction-diffusion equations of the (lambda)–(omega) type [11] in d <= 3 space dimensions, on a convex bounded domain with a C^2 boundary. The equations are close to a supercritical Hopf bifurcation in the reaction kinetics and are model equations for oscillatory reactiondiffusion equations. Global existence, uniqueness and continuous dependence on initial data of strong and weak solutions are proved using the classical Faedo-Galerkin method of Lions [15] and compactness arguments. We also present a complete case study for the application of this method to systems of nonlinear reaction-diffusion equations.