Related papers: Drift-diffusion equations on domains in $\mathbb{R…

In this article, we study domains $\Omega \subset \mathbb{S}^2$ that support positive solutions of the overdetermined problem $$ \Delta u + f(u,|\nabla u|)=0 \quad \text{in } \Omega, $$ subject to the boundary conditions $u=0$ on…

We focus on a family of nonlinear continuity equations for the evolution of a non-negative density $\rho$ with a continuous and compactly supported nonlinear mobility $\mathrm{m}(\rho)$ not necessarily concave. The velocity field is the…

The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more…

This paper proves almost-sure convergence for the self-attracting diffusion on the unit sphere $$dX(t)=\sigma dW_{t}(X(t))-a\int_{0}^{t}\nabla_{\mathbb{S}^n}V_{X_s}(X_t) dsdt,\qquad X(0)=x\in\mathbb{S}^n $$ %given by the stochastic…

We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients and unbounded divergence. In the first result we assume the drift is $L^{2}([0,T] \times \R^{d})\cap…

This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…

We investigate the strong approximation of stochastic differential equations whose drift is square-integrable in time and Dini continuous in space, while the diffusion coefficient is non-constant and uniformly elliptic. Using a refined…

We consider a generalization of classical results of Freidlin and Wentzell to the case of time dependent dissipative drifts. We show the convergence of diffusions with multiplicative noise in the zero limit of a diffusivity parameter to the…

We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be…

We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…

We study stability, long-time behavior and moment estimates for stochastic evolution equations with additive Wiener noise and with singular drift given by a divergence type quasilinear diffusion operator which may not necessarily exhibit a…

We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…

In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piece-wise continuous, and whose diffusion coefficient is superlinearly growing and locally H\"older continuous. We first…

In this article, we address the absorption properties of a class of stochastic differ- ential equations around singular points where both the drift and diffusion functions vanish. According to the H\"older coefficient alpha of the diffusion…

This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally,…

Quantum drift-diffusion equations are derived for a two-dimensional electron gas with spin-orbit interaction of Rashba type. The (formal) derivation turns out to be a non-standard application of the usual mathematical tools, such as Wigner…

Let us consider a solution of the time-inhomogeneous stochastic differential equation driven by a Brownian motion with drift coefficient $b(t,x)=\rho\,{\rm sgn}(x)|x|^\alpha/t^\beta$. This process can be viewed as a distorted Brownian…

Let $\Omega_-$ and $\Omega_+$ be two bounded smooth domains in $\mathbb{R}^n$, $n\ge 2$, separated by a hypersurface $\Sigma$. For $\mu>0$, consider the function $h_\mu=1_{\Omega_-}-\mu 1_{\Omega_+}$. We discuss self-adjoint realizations of…

This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…