On the behaviour and cases of nonexistence of the free boundary in a semibounded porous medium
type: Item
instance of: scholarly article
title: On the behaviour and cases of nonexistence of the free boundary in a semibounded porous medium
zbMATH Open document ID: 0673.35058
DOI: 10.1016/0022-247X(88)90061-3
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Consider the Cauchy-Dirichlet problem for the nonlinear Fokker-Planck equation \[ u_ t=(u^ m)_{xx}+b_ 0(u^{\lambda})_ x\quad in\quad {\mathbb{R}}^ 2_+,\quad u(x,0)=u_ 0(x),\quad x>0,\quad u(0,t)=u_ 1(t),\quad t>0, \] where \(m\geq 1\), \(\lambda >0\), \(b_ 0\in {\mathbb{R}}\), \({\mathbb{R}}^ 2_+=\{(x,t):\) \(x>0\), \(t>0\}\). This paper studies qualitative properties of the solution of this problem and, especially, the occurrence or not of the free boundaries, or interfaces, separating the sets where \(u>0\) and \(u=0\).
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 4101727
zbMATH Keywords: behavior
zbMATH Keywords: free boundary
zbMATH Keywords: semibounded porous medium
zbMATH Keywords: Cauchy-Dirichlet problem
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: qualitative properties
zbMATH Keywords: free boundaries
zbMATH Keywords: interfaces
author: J. I. Díaz
author: Robert Kersner
MaRDI profile type: Publication
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full work available at URL: 0022-247x(88)90061-3
OpenAlex ID: W2081546187
description: scientific article; zbMATH DE number 4101727