A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems.
type: Item
instance of: scholarly article
title: A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems.
zbMATH Open document ID: 1040.35146
DOI: 10.1007/PL00012596
author: Patrick Guidotti
published in: Journal of Evolution Equations
publication date: 2002-01-01T00:00:00Z
review text: The author studies a two-dimensional elliptic free boundary problem representing the quasi-steady version of diffusion of solvents through glassy polymers. The diffusion domain is initially degenerate. The normal velocity of the interface is, as usual, supposed to be proportional to a power of the solvent concentration, but here a curvature dependent term is added. The problem is reformulated in a fixed domain by means of a singular transformation, emphasizing the leading singularity. A Fourier transform technique is applied to prove existence and uniqueness of a classical solution.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1921141
zbMATH Keywords: free boundary problems
zbMATH Keywords: singular elliptic equations
zbMATH Keywords: diffusion of solvents through glassy polymers
zbMATH Keywords: Fourier transform
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: classical solution
reviewed by: Antonio Fasano
MaRDI profile type: Publication
full work available at URL: pl00012596
OpenAlex ID: W1998378225
description: scientific article; zbMATH DE number 1921141