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

Briozzo, Adriana C.Tarzia, Domingo A.2021-07-152021-07-152006-02-09Briozzo, 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. 1-16.1072-6691https://hdl.handle.net/10877/13894We 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.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalStefan problemNon-classical heat equationFree boundary problemSimilarity solutionNonlinear heat sourcesVolterra integral equationsExistence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed faceArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.