The existence of similarity solutions to a quasilinear parabolic equation
type: Item
instance of: scholarly article
title: The existence of similarity solutions to a quasilinear parabolic equation
zbMATH Open document ID: 0845.34005
published in: Differential and Integral Equations
publication date: 1996-05-09T00:00:00Z
review text: The author studies the existence of non-constant positive solutions of the differential equation \[ \triangle w+ w^p- (0, 5y\nabla w+ \lambda w) w^{- q}= 0,\quad y\in \mathbb{R}^n,\quad 0< q< 1,\quad p> 1. \] In the radially symmetric case, this problem is reduced to the investigation of the existence of positive non-constant solutions of the initial value problem \[ w''+ {n- 1\over r} w'+ w^p- \Biggl({r\over 2} w'+ \lambda w\Biggr) w^{- q}= 0,\quad w'(0)= 0,\quad w(0)= \eta> 0.\tag{\(*\)} \] New criteria for the existence (non-existence) of such solutions to the equation \((*)\) are proved.
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 856940
zbMATH Keywords: self-similar solution of the porous media equation
zbMATH Keywords: Pohozhaev identity
zbMATH Keywords: non-constant positive solutions
zbMATH Keywords: radial symmetric case
zbMATH Keywords: initial value problem
author: Yuanwei Qi
reviewed by: Elena Trofimchuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 856940