Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face

We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semi-infinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach...

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Main Authors:	Adriana C. Briozzo, Domingo A. Tarzia
Format:	Article
Language:	English
Published:	Texas State University 2006-02-01
Series:	Electronic Journal of Differential Equations
Subjects:	Stefan problem non-classical heat equation free boundary problem similarity solution nonlinear heat sources Volterra integral equations.
Online Access:	http://ejde.math.txstate.edu/Volumes/2006/21/abstr.html

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spelling	doaj-251b5160c33b44aeb2d1a83c504f51542020-11-24T22:46:49ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-02-01200621116Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed faceAdriana C. BriozzoDomingo A. TarziaWe prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semi-infinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.http://ejde.math.txstate.edu/Volumes/2006/21/abstr.htmlStefan problemnon-classical heat equationfree boundary problemsimilarity solutionnonlinear heat sourcesVolterra integral equations.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Adriana C. Briozzo Domingo A. Tarzia
spellingShingle	Adriana C. Briozzo Domingo A. Tarzia Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face Electronic Journal of Differential Equations Stefan problem non-classical heat equation free boundary problem similarity solution nonlinear heat sources Volterra integral equations.
author_facet	Adriana C. Briozzo Domingo A. Tarzia
author_sort	Adriana C. Briozzo
title	Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
title_short	Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
title_full	Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
title_fullStr	Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
title_full_unstemmed	Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
title_sort	existence and uniqueness for one-phase stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2006-02-01
description	We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semi-infinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.
topic	Stefan problem non-classical heat equation free boundary problem similarity solution nonlinear heat sources Volterra integral equations.
url	http://ejde.math.txstate.edu/Volumes/2006/21/abstr.html
work_keys_str_mv	AT adrianacbriozzo existenceanduniquenessforonephasestefanproblemsofnonclassicalheatequationswithtemperatureboundaryconditionatafixedface AT domingoatarzia existenceanduniquenessforonephasestefanproblemsofnonclassicalheatequationswithtemperatureboundaryconditionatafixedface
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Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face

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