Large deviation principle for stochastic Burgers type equation with reflection
type: Item
instance of: scholarly article
title: Large deviation principle for stochastic Burgers type equation with reflection
zbMATH Open document ID: 1485.60033
author: Ran Wang
author: Jianliang Zhai
author: Shiling Zhang
published in: Communications on Pure and Applied Analysis
publication date: 2022-01-21T00:00:00Z
review text: The authors consider a stochastic Burgers type equation on the interval \([0,1]\) with Dirichlet boundary condition and reflection. The purpose is to establish a small-noise large deviation principle for the solutions, by using the weak convergence approach. The authors adopt a new sufficient condition for the weak convergence criteria proved by \textit{A. Matoussi} et al. [Appl. Math. Optim. 83, No. 2, 849--879 (2021; Zbl 1470.60188)]. The main difficulty in the proof is to show global well-posedness and continuity of the skeleton equation, due to the highly nonlinear coefficient and the singularity caused by reflection. The authors overcome these difficulties by introducing penalized skeleton equations and showing that the limit of penalized solutions gives rise to a solution of the skeleton equation.
reviewed by: Dejun Luo
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 7461706
zbMATH Keywords: stochastic Burgers type equation
zbMATH Keywords: reflection
zbMATH Keywords: large deviation principle
zbMATH Keywords: weak convergence approach
MaRDI profile type: Publication
full work available at URL: cpaa.2021175
OpenAlex ID: W3205287547
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DOI: 10.3934/CPAA.2021175
description: scientific article; zbMATH DE number 7461706