相关论文: Boundedness of a class of discretized reaction-dif…

In this paper, we present an approach to characterising fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential…

For a nonlinear diffusion equation on graphs whose nonlinearity violates the Lipschitz condition, we prove short-time solution existence and characterize global well-posedness by establishing sufficient criteria for blow-up phenomena and…

We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

For Liouville equation with quantized singular sources, the non-simple blowup phenomenon has been a major difficulty for years. It was conjectured by the first two authors that the non-simple blowup phenomenon does not occur if the equation…

With the help of the methods developed in our previous article [Schmitz, to appear in "Annales de l'I.H.P. Prob. & Stat.], we highlight condition (T) as a source of new examples of 'ballistic' diffusions in a random environment when d>1…

The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation's method of this limit, when the…

Boundedness is an important property of many physical systems. This includes incompressible fluid flows, which are often modeled by quadratic dynamics with an energy-preserving nonlinearity. For such systems, Schlegel and Noack proposed a…

We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…

In this paper, we consider a time-fractional reaction-diffusion system with the same nonlinearities of the Newton-Leipnik chaotic system. Through analytical tools and numerical results, we derive sufficient conditions for the asymptotic…

We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…

A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reaction-diffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in…

Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…

The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…

Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional…

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…

We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N>2. This bound imply the…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

An overview of the author's papers on the new approach to the Brownian coagulation theory and its generalization to the diffusion-limited reaction rate theory is presented. The traditional diffusion approach of the Smoluchowski theory for…

We investigate the reversible diffusion-influenced reaction of an isolated pair in the presence of a non-Markovian generalization of the backreaction boundary condition in two space dimensions. Following earlier work by Agmon and Weiss, we…