A note on \(W^{\gamma}_p\)-theory of linear stochastic parabolic partial differential systems
type: Item
instance of: scholarly article
title: A note on \(W^{\gamma}_p\)-theory of linear stochastic parabolic partial differential systems
zbMATH Open document ID: 1256.60021
author: Kyeong-Hun Kim
author: Kijung Lee
published in: Stochastic Processes and their Applications
publication date: 2012-11-15T00:00:00Z
review text: The aim of the paper is to construct an \(L^p\)-theory for the general stochastic parabolic system \[ du^k= (a^{ij}_{kr}u^r_{x^ix^j} + b^i_{kr}u^r_{x^i} +c_{kr}u^r + f^k)dt + (\sigma^i_{kr,m}u^r_{x^i} +\nu_{kr,m}u^r + g^k_m)dw^m_{t} \] on \(t> 0\) and \(x\in \mathbb R^d\) with the initial conditions \(u^k(0)= u^k_0\). This system models the interactions between diffusive quantities under physical phenomena like convection. The \(L^2\)-theory for the systems of this type exists. The authors construct an \(L^p\)-theory by adopting the strategy according to which the theory of stochastic partial differential equations is constructed.
reviewed by: Ruhollah Jahanipur
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35K45
zbMATH DE Number: 6106882
zbMATH Keywords: linear stochastic parabolic partial differential system
zbMATH Keywords: \(W_p^{\gamma}\) theory
MaRDI profile type: Publication
full work available at URL: j.spa.2012.08.016
OpenAlex ID: W2063898356
DOI: 10.1016/J.SPA.2012.08.016
description: scientific article; zbMATH DE number 6106882