An implicit two-phase free boundary problem for the heat equation
type: Item
instance of: scholarly article
title: An implicit two-phase free boundary problem for the heat equation
zbMATH Open document ID: 1064.35217
author: Nguyen Dinh Tri
author: Nguyen Dinh Binh
published in: Vietnam Journal of Mathematics
publication date: 2005-02-11T00:00:00Z
review text: The authors prove existence and uniqueness of a classical solution to the following free boundary problem \[ u_{xx}-u_t=0, \quad 0<x<s(t), \] \[ \gamma v_{xx}-v_t=0, \quad s(t)<x<1, \] \[ s(0)=b, \quad 0<b<1, \] \[ u(x,0)=\phi(x), \quad 0<x<b, \] \[ v(x,0)=\psi(x), \quad b<x<1, \] \[ u_x(0,t)=f(t), \quad v(1,t)=F(t), \] \[ u(s(t),t)=v(s(t),t)=0, \] \[ u_x(s(t),t)-v_x(s(t),t)=\lambda s(t). \]
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 2133570
zbMATH Keywords: oxygen diffusion-consumption problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: classical solution
reviewed by: Mykola Krasnoschok
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2133570