A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face
type: Item
instance of: scholarly article
title: A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face
zbMATH Open document ID: 1120.35085
author: Adriana C. Briozzo
author: Domingo A. Tarzia
published in: Applied Mathematics and Computation
publication date: 2007-01-09T00:00:00Z
review text: The following non-classical free boundary problem is considered \[ u_t-u_{xx}=-F(u(0,t)),\quad 0<x<s(t),\,\,\, 0<t<T, \] \[ u(x,0)=h(x),\;\;0<x<s(0),\quad u_x(0,t)=-g(t)\leq 0,\,0<t<T, \] \[ u(s(t),t)=0,\quad u_x(s(t),t)=-s'(t). \] The authors reduce this problem to a system of two Volterra integral equations and prove the existence and uniqueness of the classical solution.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 5083735
zbMATH Keywords: Stefan problem
zbMATH Keywords: non-classical heat equation
zbMATH Keywords: free boundary problem
zbMATH Keywords: similarity solution
zbMATH Keywords: nonlinear heat sources
zbMATH Keywords: Volterra integral equation
reviewed by: Mykola Krasnoschok
MaRDI profile type: Publication
full work available at URL: j.amc.2006.04.043
OpenAlex ID: W2080530205
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DOI: 10.1016/J.AMC.2006.04.043
description: scientific article; zbMATH DE number 5083735