Self-similar solutions to the Cauchy problem for a nonlinear heat equation
type: Item
instance of: scholarly article
title: Self-similar solutions to the Cauchy problem for a nonlinear heat equation
zbMATH Open document ID: 0955.35041
author: A. N. Vasil'ev
author: A. P. Mikhailov
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-10-11T00:00:00Z
review text: All possible power-scaling self-similar solutions to the Cauchy problem for a one-dimensional nonlinear heat equation with power nonlinearity are analyzed on the time interval \(0<t<+\infty\) in Cartesian, cylindrical, and spherical coordinates. The existence conditions and the properties of the solutions are determined as depending on the parameters of the problem. A number of new heating and cooling modes are found.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 80M35
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1472904
zbMATH Keywords: power nonlinearity
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: new heating and cooling modes
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1472904