Exact non-self-similar solutions of the equation \(u_t=\Delta\ln u\)
type: Item
instance of: scholarly article
title: Exact non-self-similar solutions of the equation \(u_t=\Delta\ln u\)
zbMATH Open document ID: 1028.35083
DOI: 10.1023/A:1012943313941
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: This paper is devoted to the construction of exact, non-self-similar, anisotropic (in the sense of variables), explicit, nonnegative solutions of the nonlinear diffusion (heat) equation \[ u_t=\Delta\ln u\tag{1} \] where \(u= u(x,t): \Omega\times \mathbb{R}^+\to \mathbb{R}\), \(x\in\mathbb{R}^n\), \(\Omega\subset\mathbb{R}^n\) is the domain and \(\mathbb{R}^+= \{t\mid 0\leq t<\infty\}\), \(u(x,t)\geq 0\) is the temperature of the medium.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 1927831
zbMATH Keywords: anisotropic nonnegative solutions
zbMATH Keywords: nonlinear diffusion equation
author: Gennady Alekseevich Rudykh
author: Edward Ivanovich Semenov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1012943313941
OpenAlex ID: W2912035241
description: scientific article; zbMATH DE number 1927831