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In this paper, we show that the $L^1$ norm of the bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form u_t + div f(x,t,u) = div(|u|^{\alpha}\nabla u),   x \in R^n , t > 0, where \alpha > 0 is constant, decrease, under fairly broad conditions in advection flow f . In addition, we derive the mass conservation property for positive (or negative) solutions.

Decreasing of the L^1 norm and mass conservation for Porous Medium Equations with advection