相关论文: Stationary spatial structures in reaction-subdiffu…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
We consider the coagulation dynamics A+A -> A and A+A <-> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems,…
We study reaction zones in three different versions of the A+B->0 system. For a steady state formed by opposing currents of A and B particles we derive scaling behavior via renormalization group analysis. By use of a previously developed…
We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
In this paper we study a class of stationary states for reaction--diffusion systems of $k\geq 3$ densities having disjoint supports. For a class of segregation states governed by a variational principle we prove existence and provide…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time…
We investigate the A+B=0 bimolecular chemical reaction taking place in low-dimensional spaces when the mobilities of the two reacting species are not equal. While the case of different reactant mobilities has been previously reported as not…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal…
Diffusion and reaction of initially separated ions A- and B+ in the presence of counter ions A'+ and B'- is studied. The dynamics is described in terms of reaction-diffusion equations obeying local electroneutrality, and the time-evolution…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…