Traveling wave solutions of the porous medium equation with degenerate interfaces
type: Item
instance of: scholarly article
title: Traveling wave solutions of the porous medium equation with degenerate interfaces
zbMATH Open document ID: 1284.34035
author: L. Paudel
author: Joseph A. Iaia
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2013-03-04T00:00:00Z
review text: Consider the partial differential equation \[ {\partial v\over\partial t}= (m- 1)v\,\Delta v+ |\nabla v|^2.\tag{\(*\)} \] The authors look for a solution of \((*)\) of the form \[ v(x,y,z,t)= \sqrt{x^2+ y^2+(z-ct)^2}\,F\Biggl(\tan^{-1}\Biggl({\sqrt{x^2 +y^2}\over z- ct}\Biggr)\Biggr),\tag{\(**\)} \] where \(c> 0\) is the speed of the corresponding traveling wave. Substituting \((**)\) into \((*)\) one get a differential equation for \(F\). The authors study the existence of a positive solution to appropriate boundary value problems.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 6140768
zbMATH Keywords: porous medium equation
zbMATH Keywords: reduction to ODE
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: j.na.2012.10.016
OpenAlex ID: W2048778762
DOI: 10.1016/J.NA.2012.10.016
description: scientific article; zbMATH DE number 6140768