Existence, uniqueness and an explicit solution for a one phase Stefan problem for a non-classical heat equation

A.C. BRIOZZO - D.A. TARZIA

Coimbra (Portugal)

Congreso; International Conference on Free Boundary Problems: Theory and Applications; 2006

Comunidad Free Boundary Problems

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 is obtained by using the Friedman-Rubinstein integral representation method through an equivalent system of two Volterra integral equations. Moreover, an explicit solution of a similarity type is presented for a non-classical heat source depending on time and heat flux on the fixed face x=0.