Geodesic
Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 35R35, 80A22, 35C05, 35K20, 35K55, 45G15, 35C15
Keywords: Stefan problem, non-classical heat equation, free boundary problem, similarity solution, nonlinear heat sources, Volterra integral equations 
@article{EJDE_2006__2006__a65,
     author = {Briozzo,  Adriana C. and Tarzia,  Domingo A.},
     title = {Existence and uniqueness for one-phase {Stefan} problems of nonclassical heat equations with temperature boundary condition at a fixed face},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1092.35117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a65/}
}
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%J Electronic journal of differential equations
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Briozzo,  Adriana C.; Tarzia,  Domingo A. Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a65/