The expanding behavior of positive set H u (t) of a degenerate parabolic equation

This work studies the expanding behavior of the positive set of solutions and the continuous dependence on the nonlinearity for a degenerate parabolic partial differential equation u_t=Df(u){u_{t}=\Delta\phi(u)} . Our objective is to give an explicit expression of speed of propagation of the solution and to show that the solution continuously depends on the nonlinearity of the equation.