Abstract: The property of the viscosity solutions of the Cauchy problem of a degenerate parabolic equation not in divergence form is studied. The viscosity solution means a weak solution in the distribution sense obtained by the vanishing viscosity method. Using some techiques of studying weak solutions and establishing some estimates on the viscosity solution, we prove the continuity of the viscosity solution with respect to aparameter contained in the equations.

Key words: viscosity solution, not in divergence form, degenerate parabolic equation, continuity