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

A.C. BRIOZZO - D.A. TARZIA

Electronic Journal of Differential Equations

Texas Univ. (USA)

Lugar: Texas; Año: 2006 vol. 2006 p. 1 - 16

We prove the 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 with temperature boundary condition at the fixed face x=0 . 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.