Nonlinear reaction diffusion schemes in continuous kinetics

We analyze reaction schemes in continuous mixtures in the presence of space gradients from the standpoint of the Banach theorem of contractive mappings. The particular case of reaction-diffusion kinetics in a catalyst pellet (slab-model) is considered by developing in detail the analysis for monotonically decaying kinetics and for generic (mass-conserving) reaction schemes. The latter case is addressed by making use of the Frechet decomposition theorem of continuous functionals. Kinetic schemes for which the conservation principle in continuous mixtures cannot be expressed in a straightforward manner are also discussed, focusing attention on the intrinsic dynamic complexity (instabilities, chaos, stochastic description) induced by continuous parametrization.