Wave Bifurcation in Models for Heterogeneous Catalysis

Heterogeneous Catalysis means that the reacting species and the catalyst do not have the same phase. A mathematical model for such a reaction has to take into account as well the complex kinetic processes and the spatial coupling. Depending on how strong the reactants are bound to the surface of the catalyst, the diffusion coefficients may vary by orders. Diffusion does not only smoothen the concentration gradients which are given by the initial data or result from the reaction kinetic processes. It is also able to induce instabilities which give rise to stable inhomogeneous steady or time-periodic solutions. The conditions for such a bifurcation are rather restrictive but can be checked by only considering the kinetic part. Numerical simulations can be carried out more precisely in the neighborhood of the critical parameters. 1. Diffusion-Induced Instabilities Diffusion-induced instability or Turing instability means that for a reactiondiffusion system of at least two scalar equations there is a spatially constant steady solution which is asymptotically stable in the sense of linearized stability in the space of constant functions. Nevertheless, it is unstable to spatially inhomogeneous perturbations. Consider a parameter dependent system of N equations on a bounded domain with appropriate boundary conditions