Averaging for fundamental solutions of parabolic equations
type: Item
instance of: scholarly article
title: Averaging for fundamental solutions of parabolic equations
zbMATH Open document ID: 0911.35057
author: Michael A. Kouritzin
published in: Journal of Differential Equations
publication date: 1999-05-04T00:00:00Z
full work available at URL: http://purl.umn.edu/2905
review text: A parabolic operator of order \(2p\) depending on the small parameter \(\varepsilon\) \[ \partial_t-\sum_{q\leq 2p}A_q(x,t/\varepsilon)\partial^q_x \] is considered in \(d\)-dimensional \(x\)-space. The coefficients \(A_q\) depend on the fast time under basic hypothesis that there exists an averaging: \[ \int^t_0\bigl[A_q(x,s/\varepsilon)-A^0_q(x)\bigr]ds\to 0\quad\text{as }\varepsilon\to 0. \] The corresponding parabolic operator with the coefficients \(A^0_q\) is taken and two fundamental solutions \(\Gamma_\varepsilon\), \(\Gamma_0\) are considered. The main goal of the paper is justification of the convergence \(\partial^j_x(\Gamma_\varepsilon-\Gamma_0)\to 0\) as \(\varepsilon\to 0\), \((0\leq j\leq 2p-1)\).
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35E05
zbMATH DE Number: 1014431
zbMATH Keywords: fast oscillation
MaRDI profile type: Publication
OpenAlex ID: W1999214603
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DOI: 10.1006/JDEQ.1996.3244
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description: scientific article; zbMATH DE number 1014431