Asymptotic estimates of solutions of \(u_ t - \frac12\Delta u =-|\nabla u|\) in \(\mathbb{R}_ + \times \mathbb{R}^ d,\quad d\geq 2\)
type: Item
instance of: scholarly article
title: Asymptotic estimates of solutions of \(u_ t - \frac12\Delta u =-|\nabla u|\) in \(\mathbb{R}_ + \times \mathbb{R}^ d,\quad d\geq 2\)
zbMATH Open document ID: 0869.35052
published in: Journal of Functional Analysis
publication date: 1997-06-24T00:00:00Z
review text: The authors express the solution \(u_\mu\) of \(u_t -\frac{1}{2}\triangle u =-|\nabla u|\) in \(\mathbb{R}_+ \times \mathbb{R}^d, \;d\geq 2; \;u_\mu(0,.)=\mu\) by a functional of a \(d\)-dimensional Bessel process, where \(\mu\) is invariant by rotations and profiled. Using this result they estimate the asymptotic behaviour of \(|u_\mu (t,\cdot)|_1\) and \(|u_\mu (t,\cdot)|_\infty\) as \(t\) goes to infinity.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 992046
zbMATH Keywords: \(d\)-dimensional Bessel process
zbMATH Keywords: probabilistic representation
author: Said Benachour
author: Bernard Roynette
author: Pierre Vallois
MaRDI profile type: Publication
full work available at URL: jfan.1996.2984
OpenAlex ID: W142737174
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DOI: 10.1006/JFAN.1996.2984
description: scientific article; zbMATH DE number 992046