title: Reaction-diffusion processes with nonlinear diffusion.
abstract: We study reaction-diffusion processes with concentration-dependent diffusivity. First, the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes is determined. We then consider two natural inhomogeneous realizations. The two-species annihilation process is investigated in the situation when the reactants are initially separated, namely each species occupies a half space. In particular, we establish the growth law of the width of the reaction zone. The single-species annihilation process is studied in the situation when the spatially localized source drives the system toward the nonequilibrium steady state. Finally, we investigate a dissolution process with a localized source of diffusing atoms which react with the initially present immobile atoms forming immobile molecules.
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D004058:Diffusion; D004305:Dose-Response Relationship, Drug; D008956:Models, Chemical; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D013696:Temperature