Related papers: Exact Solutions of Low-Dimensional Reaction-Diffus…
In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy…
We consider general models of coupled reaction-diffusion systems for interacting variants of the same species. When the total population becomes large with intensive competition, we prove that the frequencies (i.e. proportions) of the…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…
A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for…
The fast-reaction limit for reaction--diffusion systems modelling predator--prey interactions is investigated. In the considered model, predators exist in two possible states, namely searching and handling. The switching rate between these…
Using a normal form approach described in a previous paper we derive an amplitude equation for a reaction-diffusion system with a Hopf bifurcation coupled to one or more slow real eigenmodes. The new equation is useful even for systems…
A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to…
We have previously discussed the one-dimensional multitrap system of finite range and found the somewhat unexpected result that the larger is the number of imperfect traps the higher is the transmission through them. We discuss in this work…
We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first…
Some models of diffusion-limited reaction processes in one dimension lend themselves to exact analysis. The known approaches yield exact expressions for a limited number of quantities of interest, such as the particle concentration, or the…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…