Free Boundary Problem for Degenerate Quasilinear Parabolic Equations

摘要

This paper is concerned with a free boundary problem which arises in the study of a class of degenerate parabolic equations. A thorough treatment is given for a special case which can be reduced to a problem in ordinary differential equations upon introduction of the appropriate similarity variable. Beyond its inherent interest, the solvability of the resulting problem establishes that an analysis by Vol'pert and Hudjaev of jump conditions satisfied by solutions of degenerate parabolic equations is not correct in general. (Author)