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. <i>Electronic Journal of Differential Equations, 2006</i>(21), pp. 1-16.

Rights

Attribution 4.0 International

Rights Holder

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights License