Related papers: Global martingale solutions for a stochastic popul…
The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance…
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the…
We solve explicitly the following problem: for a given probability measure mu, we specify a generalised martingale diffusion X which, stopped at an independent exponential time T, is distributed according to mu. The process X is specified…
The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with a tri-diagonal Toeplitz matrix of diffusion coefficients and prove the global existence of solutions using Lyapunov…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
This paper considers a stochastically perturbed Keller-Segel-Navier-Stokes (KS-SNS) system arising from the biomathematics in two dimensions, where the diffusion of fluid is expressed by a fractional Laplacian with an exponent in $[1/2,1]$.…
We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction.…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth. The mathematical challenge is due to the fact that the…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with…
In this paper we consider a stochastic thin-film equation with a one dimensional Gaussian Stratonovych noise. We establish the existence of non-negative global weak martingale solution, and study its long time asymptotic properties. In…
The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove…
This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time $L^1$ a-priori estimates, for instance, as a consequence of suitable mass conservation…
Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the…
We study the global existence of classical solutions to volume-surface reaction-diffusion systems with control of mass. Such systems appear naturally from modeling evolution of concentrations or densities appearing both in a volume domain…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…