On symmetrization in the single-phase Stefan problem
type: Item
instance of: scholarly article
title: On symmetrization in the single-phase Stefan problem
zbMATH Open document ID: 0716.35086
author: R. Yu. Nabokov
published in: Moscow University Mathematics Bulletin
publication date: 1990-01-01T00:00:00Z
review text: The investigated problem is as follows: to obtain such function \(u>0\) for which \[ u_ t-\partial_ i(a_{ij}(x,t,u)\partial_ ju=f(x,t),\quad f\geq 0\text{ on } G\subset {\mathbb{R}}^ n\times {\mathbb{R}}_+ \] with initial condition \(u|_{t=0}=u_ 0(x)\) and Stefan condition on the free boundary; \(a_{ij}\partial_ ju\partial \phi =\mu \phi_ t\), \(\mu >0\), where the unknown free boundary \(\Gamma\) is given by the equation \(\phi (t,x)=0\) and \(a_{ij}\) assumed to be elliptic. The tool of solution of this problem is the following: Instead of the original problem the solution of the symmetrized problem is investigated in which the domain \(\tilde G,\) \(\tilde a_{ij}\) and \(\tilde u_ 0\) are assumed to be symmetric. In this paper a theorem is proved which says: The norm of solution of the original problem can be estimated by the norm of solution of the symmetrized problem.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 4179975
zbMATH Keywords: Stefan problem
zbMATH Keywords: comparison result
zbMATH Keywords: symmetrized problem
reviewed by: Gy. Molnárka
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4179975