A Class of Degenerate Totally Nonlinear Parabolic Equations

Of concern is the following totally nonlinear parabolic equation, as well as its higher space dimensional analogue ut x,t.sb f x,ux.ux xqf x,u,ux.., x,t.g 0, 1.= 0, `. j ux j,t.g y1. bj u j, t.., js0, 1 u x, 0.su0 x.. Here b0and b1are maximal monotone graphs in R=R, and b t. or bX t. might equal zero for some t, at which the equation is not uniformly parabolic. It is shown by the method of lines and nonlinear operator semigroup theory that the equation has a unique global solution