Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach
type: Item
instance of: scholarly article
title: Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach
zbMATH Open document ID: 0935.35010
author: Etienne Pardoux
published in: Journal of Functional Analysis
publication date: 2000-04-19T00:00:00Z
review text: Second-order parabolic linear and semilinear equations are considered with rapidly oscillating periodic coefficients. The solutions are proved to converge to solutions of a limiting equation with constant coefficients being the averages in some sense of the corresponding coefficients of the original equation. The methods of proofs are of probabilistic nature. For the linear equation the Feynman-Kac formula is used, and for the semilinear equations the solutions are represented by means of backward stochastic differential equations.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 1367856
zbMATH Keywords: rapidly oscillating periodic coefficients
zbMATH Keywords: Feynman-Kac formula
zbMATH Keywords: averages
reviewed by: Marek Capiński
MaRDI profile type: Publication
OpenAlex ID: W2092709451
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DOI: 10.1006/JFAN.1999.3441
description: scientific article; zbMATH DE number 1367856