Related papers: Weak mean random attractors for non-local random a…
We study a Stochastic Landau-Lifschitz Equation with non-zero anisotrophy energy and multidimensional noise. The existence and some regularities of weak solution have been proved.
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii)…
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…
We consider invertible linear maps with additive spherical bounded noise. We show that minimal attractors of such random dynamical systems are unique, strictly convex and have a continuously differentiable boundary. Moreover, we present an…
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fokker-Planck equation. First, we prove a superposition…
We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random…
We consider weakly damped nonlinear Schr\"odinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero…
We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement,…
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…
We prove the existence and weak uniqueness of weak solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class with mixed norms.
We establish the existence of weak solutions to a class of distribution-dependent stochastic differential equations (DDSDEs) with possibly degenerate multiplicative noise and singular coefficients. Extending the weak existence techniques…
We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…
We develop a "weak Wa\.zewski principle" for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a…
The long time behavior of Wong-Zakai approximations of 2D as well as 3D non-autonomous stochastic convective Brinkman-Forchheimer (CBF) equations with non-linear diffusion terms on bounded and unbounded ($\mathbb{R}^d$ for $d=2,3$) domains…
In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from…
We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy…
We investigate an evolutive system of non-linear partial differential equations derived from Oldroyd models on Non-Newtonian flows. We prove global existence of weak solutions, in the case of a smooth bounded domain, for general initial…
We extend our recently introduced stochastic nonlocal traffic flow model to more general random perturbations, including Markovian noise derived from a discretized Jacobi-type stochastic differential equation. Invoking a deterministic…
Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection and the so-called submartingale problem. We introduce a general formulation of the submartingale problem for…