Related papers: Large deviations for fast transport stochastic RDE…
We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
In this paper we prove the well-posedness of non-autonomous deterministic and stochastic reaction-diffusion equations with a polynomial reaction term. Concerning the stochastic problem, we also prove a new result on the space-time…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Singular limit problems of reaction-diffusion systems have been studied in cases where the effects of the reaction terms are very large compared with those of the other terms. Such problems appear in literature in various fields such as…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
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…
We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…