Stochastic parabolic equations with singular potentials
نویسندگان
چکیده
In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and initial condition. For the analysis these combine chaos expansion method from white noise concept very weak solutions. given equation introduce notion solution, prove existence uniqueness solution to corresponding value problem show its independence regularization on potential. addition, consistency is shown.
منابع مشابه
On Nonexistence of Baras–goldstein Type for Higher-order Parabolic Equations with Singular Potentials
The celebrated result by Baras and Goldstein (1984) established that the heat equation with singular inverse square potential in a smooth bounded domain Ω ⊂ RN , N ≥ 3, such that 0 ∈ Ω, ut = Δu+ c |x|2 u in Ω× (0, T ), u ∣∣ ∂Ω = 0, in the supercritical range c > cHardy(1) = ( N−2 2 )2 , does not have a solution for any nontrivial L1 initial data u0(x) ≥ 0 in Ω or for a positive measure. Namely,...
متن کاملAPPROXIMATION OF STOCHASTIC PARABOLIC DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT FINITE DIFFERENCE SCHEMES
We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.
متن کاملNonlinear Parabolic Equations with Cc Adll Ag Noise Stochastic Parabolic Equations
We dispense with semimartingale (and Dirichlet process) assumptions while investigating arbitrary-order stochastic semi-linear parabolic equations. The emergence of fractional L evy processes in pressing applications like communication networks and mathematical nance highlights the need for studying stochastic evolutionary equations under general noise conditions. Our principle result states th...
متن کاملFluctuations of Parabolic Equations with Large Random Potentials
In this paper, we present a fluctuation analysis of a type of parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan’s method, and a quantitative martingale central limit theorem, we derive the asymptotic distribution of the rescaled error between heterogeneous and homogenized solutions under ...
متن کاملStanding waves for nonlinear Schrödinger equations with singular potentials
We study semiclassical states of nonlinear Schrödinger equations with anisotropic type potentials which may exhibit a combination of vanishing and singularity while allowing decays and unboundedness at infinity. We give existence of spike type standing waves concentrating at the singularities of the potentials. © 2008 Elsevier Masson SAS. All rights reserved. Résumé Nous étudions les états semi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos Solitons & Fractals
سال: 2021
ISSN: ['1873-2887', '0960-0779']
DOI: https://doi.org/10.1016/j.chaos.2021.111245