Nonlinear diffusion in the presence of fast reaction

A kinetic reaction model: Decay to equilibrium and macroscopic limit

“…In Section 1.3 the macroscopic/fast-reaction limit is carried out formally, leading to a nonlinear diffusion equation for the difference of the position densities of the reactants. Similar results have been derived for reaction-diffusion systems [2,11] and for coagulation-fragmentation models [3,4]. A rigorous justification of the limit is the subject of Section 3.…”

Diffusion in an annihilating environment

“…However, most of the literature on equations of type (1.1) (see e.g. Hilhorst et al [9], [10], [11] and references therein) deals with equations without the δ-source, which plays a central role in our results.…”

Mathematical analysis of a model describing the invasion of bacteria in burn wounds

“…This condition reduces to a transmission condition across the free boundary in the case that d > 0 (see Remark 2) and to a Stefan condition in the case that d = 0 with the initial data being that from the biological model. Related results were proven before; we refer to [DHMP99], [CDH + 04] and [HIMN01] for the case that d > 0 and to [HvdHP00], [HvdHP97], [HvdHP96] and [EHvdHP01] for the case that d = 0, but this is the first time that a single expression has been given for the limit problem which permits in particular the recovery both of a two-phase Stefan problem with 'zero latent heat' in the case that d > 0 and of a one-phase Stefan problem in the case that d = 0 with the special initial condition holding.…”