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Existence, Uniqueness and an Explicit Solution for a One-Phase Stefan Problem for a Non-classical Heat Equation

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Free Boundary Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 154))

Abstract

Existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material is obtained by using the Friedman-Rubinstein integral representation method through an equivalent system of two Volterra integral equations. Moreover, an explicit solution of a similarity type is presented for a non-classical heat source depending on time and heat flux on the fixed face x = 0.

It was supported by CONICET PIP No. 3579 and ANPCYT PICT No. 03-11165.

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Author information

Authors and Affiliations

  1. Depto. Matemática, FCE, Univ. Austral, Paraguay 1950, S2000FZF, Rosario, Argentina

    Adriana C. Briozzo

  2. Depto. Matemática — CONICET, FCE, Univ. Austral, Paraguay 1950, S2000FZF, Rosario, Argentina

    Domingo A. Tarzia

Authors
  1. Adriana C. Briozzo
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  2. Domingo A. Tarzia
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Editor information

Editors and Affiliations

  1. Departamento de Matemática Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal

    Isabel Narra Figueiredo

  2. Universidade de Lisboa / CMAF, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    José Francisco Rodrigues

  3. Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Lisa Santos

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Briozzo, A.C., Tarzia, D.A. (2006). Existence, Uniqueness and an Explicit Solution for a One-Phase Stefan Problem for a Non-classical Heat Equation. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_12

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