Time--space white noise eliminates global solutions in reaction diffusion equations
, 2008 We prove that perturbing the reaction--diffusion equation $u_t=u_{xx} + (u_+)^p$ ($p>1$), with time--space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive ...
Bandle +19 more
core +1 more source
On a stochastic partial differential equation with non-local diffusion
, 2005 In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one.
C. Bardos +16 more
core +1 more source
On the multifractal local behavior of parabolic stochastic PDEs
, 2017 Consider the stochastic heat equation $\dot{u}=\frac12 u"+\sigma(u)\xi$ on $(0\,,\infty)\times\mathbb{R}$ subject to $u(0)\equiv1$, where $\sigma:\mathbb{R}\to\mathbb{R}$ is a Lipschitz (local) function that does not vanish at $1$, and $\xi$ denotes ...
Huang, Jingyu, Khoshnevisan, Davar
core +1 more source
Decorrelation of total mass via energy [PDF]
, 2014 The main result of this small note is a quantified version of the assertion that if u and v solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of ...
Chen, Le +2 more
core
On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data
, 2007 Consider an inviscid Burgers equation whose initial data is a Levy a-stable process Z with a > 1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller ...
A.A. Novikov +17 more
core +3 more sources
Approximations of Stochastic Partial Differential Equations [PDF]
, 2014 In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks.
Di Nunno, Giulia, Zhang, Tusheng
core +1 more source
Global solutions of aggregation equations and other flows with random diffusion. [PDF]
Probab Theory Relat Fields, 2023 Rosenzweig M, Staffilani G.
europepmc +1 more source
Stochastic differential equation modelling of cancer cell migration and tissue invasion. [PDF]
J Math Biol, 2023 Katsaounis D +2 more
europepmc +1 more source
Well-posedness for a stochastic 2D Euler equation with transport noise. [PDF]
Stoch Partial Differ Equ, 2023 Lang O, Crisan D.
europepmc +1 more source
Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. [PDF]
Stoch Partial Differ Equ, 2022 Harbrecht H, Schmidlin M.
europepmc +1 more source