Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face
Date
2006-02-09
Authors
Briozzo, Adriana C.
Tarzia, Domingo A.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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.
Description
Keywords
Stefan problem, Non-classical heat equation, Free boundary problem, Similarity solution, Nonlinear heat sources, Volterra integral equations
Citation
Briozzo, A. C., & Tarzia, D. A. (2006). 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, 2006(21), pp. 1-16.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.