Abstract :
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
