Related papers: Diffusion-controlled reactions with non-Markovian …
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a…
We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski who recognized the importance of diffusion in chemical reactions, we discuss…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. The lack of consensus is mostly caused…
We consider steady-state diffusion in a bounded planar domain with multiple small targets on a smooth boundary. Using the method of matched asymptotic expansions, we investigate the competition of these targets for a diffusing particle and…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…
In this paper we extend the encounter-based model of diffusion-mediated surface absorption to the case of an unbiased run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ and switching between two constant velocity states…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an…
We consider a $4\times4$ nonlinear reaction-diffusion system posed on a smooth domain $\Omega$ of $\mathbb{R}^N$ ($N \geq 1$) with controls localized in some arbitrary nonempty open subset $\omega$ of the domain $\Omega$. This system is a…
We study the asymptotic speed of traveling fronts of the scalar reaction diffusion for positive reaction terms and with a diffusion coefficient depending nonlinearly on the concentration and on its gradient. We restrict our study to…
Back-diffusion is the phenomenon by which random walkers revisit binding sites on a lattice. This phenomenon must occur on interstellar dust particles, slowing down dust-grain reactions, but it is not accounted for by standard rate-equation…