Related papers: Finite time extinction for stochastic sign fast di…

We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…

For a smooth bounded domain $\Omega\subseteq\mathbb{R}^n$, $n\geq 3$, we consider the fast diffusion equation with critical sobolev exponent $$\frac{\partial w}{\partial\tau} =\Delta w^{\frac{n-2}{n+2}}$$ under Dirichlet boundary condition…

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…

In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…

We investigate the homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=\Delta u^m$, posed in a smooth bounded domain $\Omega\subset \mathbb{R}^N$, in the exponent range $m_s=(N-2)_+/(N+2)<m<1$. It is known that bounded…

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

We consider the Schrodinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time,…

Inspired by recently developed Fokker--Planck models for Bose--Einstein statistics, we study a consensus formation model with condensation effects driven by a polynomial diffusion coefficient vanishing at the domain boundaries. For the…

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 consider a nonlinear Schrodinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra…

For a large class of non-negative initial data, the solutions to the quasilinear viscous Hamilton-Jacobi equation $\partial\_t u-\Delta\_p u+|\nabla u|^q=0$ in $(0,\infty)\times\real^N$ are known to vanish identically after a finite time…

Motivated by studies of stochastic systems describing non-equilibrium dynamics of (real-valued) spins of an infinite particle system in $\mathbb{R}^n$ we consider a row-finite system of stochastic differential equations with dissipative…

We prove the global space-time bound for the mass critical nonlinear Schr\"odinger equation perturbed by a small multiplicative noise in dimension three. The associated scattering behavior are also obtained. We also prove a global…

We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any…

We study the asymptotics of Allen-Cahn-type bistable reaction-diffusion equations which are additively perturbed by a stochastic forcing (time white noise). The conclusion is that the long time, large space behavior of the solutions is…

The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existence and uniqueness of the local-in-time weak solution for…

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…

We consider a class of $L^1$ critical nonlocal aggregation equations with linear or nonlinear porous media-type diffusion which are characterized by a long-range interaction potential that decays faster than the Newtonian potential at…

In this article, we prove that small localized data yield solutions to Higher order Korteweg-de Vries type equation with scattering-supercritical nonlinearity have linear dispersive decay in only a finite length of time. The proof is done…

The aim of this paper is to study the finite space blow up of the solutions for a class of fourth order differential equations. Our results answer a conjecture in [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions…