Self-similar solutions for a nonlinear degenerate parabolic equation
type: Item
instance of: scholarly article
title: Self-similar solutions for a nonlinear degenerate parabolic equation
zbMATH Open document ID: 1130.35085
author: Chein-Shan Liu
published in: Lobachevskii Journal of Mathematics
publication date: 2007-04-11T00:00:00Z
full work available at URL: https://eudml.org/doc/224731
full work available at URL: 50.html
review text: This paper concerns the self-similar solution of the doubly nonlinear degenerate parabolic equation in \(\mathbb R^n\) \[ \frac{\partial u}{\partial t} = \text{div}(| x| ^\alpha| \nabla(| u| ^{m-1} u)| ^{N-1}\nabla(| u| ^{m-1}u)). \] The author proves the existence of the nonnegative self-similar solution of the form \[ u(x,t) = u_0 t^{\gamma}y(c| x| t^{-\beta}), \] where \(y \in C^1([0,+\infty))\), \(m >1,\;N >1\), \(\gamma > 0\), \(u_0 > 0\), \(\beta= \frac{\gamma(mN-1)+1}{N-\alpha+1}\), \(c^{N+1}=u_0^{mn-1}\beta,\) and \( \frac {\gamma}{\beta} \geq -n.\)
reviewed by: Shigeru Sakaguchi
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 5141822
zbMATH Keywords: doubly nonlinear equation
zbMATH Keywords: nonnegative solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5141822