Related papers: Global in time solutions to stochastic reaction-di…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
This paper investigates a stochastic parabolic system under Robin boundary conditions, for which the deterministic counterpart exhibits finite quenching. The stochastic system incorporates mixed noise, combining standard one-dimensional…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the…
We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a…
Aggregation equations, such as the parabolic-elliptic Patlak-Keller-Segel model, are known to have an optimal threshold for global existence vs. finite-time blow-up. In particular, if the diffusion is absent, then all smooth solutions with…
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…
We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…
Reaction-diffusion systems which include processes of the form A+A->A or A+A->0 are characterised by the appearance of `imaginary' multiplicative noise terms in an effective Langevin-type description. However, if `real' as well as…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or…
Models issued from ecology, chemical reactions and several other application fields lead to semi-linear parabolic equations with super-linear growth. Even if, in general, blow-up can occur, these models share the property that mass control…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem…
We consider an infinite-dimensional dynamical system with polynomial nonlinearity and additive noise given by a finite number of Wiener processes. By studying how randomness is spread by the system we develop a counterpart of Hormander's…
In this paper, we study the stochastic degenerate Keller-Segel system perturbed by linear multiplicative noise in a bounded domain $\mathcal{O}$. We establish the global existence of martingale solutions for this model with any nonnegative…