Generalized solutions of degenerate second-order quasilinear parabolic and elliptic equations

Abstract

Generalized (entropy) solutions of degenerate second-order quasilinear parabolic and elliptic equations are considered. In classes of functions under consideration it is proved that a function is a generalized solution if and only if it is a weak solution and satisfies discontinuity conditions. Uniqueness and stability of the generalized solution of the Cauchy problem for a degenerate parabolic equation is proved.