Large time asymptotics for fundamental solutions of diffusion equations
type: Item
instance of: scholarly article
title: Large time asymptotics for fundamental solutions of diffusion equations
zbMATH Open document ID: 0588.35044
author: Minoru Murata
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: This paper gives asymptotic estimates for U(x,y,t) which is the fundamental solution for the parabolic operator \[ \partial /\partial t- \sum^{n}_{j,k=1}a_{jk}(x)\partial^ 2/\partial x_ j\partial x_ k+\sum^{n}_{j=1}b_ j(x)\partial /\partial x_ j+c(x),\quad x\in {\mathbb{R}}^ n,\quad t>0. \] These estimates are for large values of t. Specific estimates are given for these asymptotic forms which involve negative powers of t (for n odd) and negative powers of t multiplied by positive powers of log t (for n even). The cases c(x)\(\equiv 0\), \(c(x)<0\), \(c(x)>0\) are discussed separately.
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 3944393
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: asymptotic estimates
zbMATH Keywords: fundamental solution
zbMATH Keywords: parabolic operator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228678
OpenAlex ID: W2013550248
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DOI: 10.2748/TMJ/1178228678
description: scientific article; zbMATH DE number 3944393