An error estimate for viscous approximate solutions of degenerate parabolic equations

Relying on recent advances in the theory of entropy solutions for nonlinear (strongly) degenerate parabolic equations, we present a direct proof of an L1 error estimate for viscous approximate solutions of the initial value problem for ∂tw + div V (x)f(w) = ∆A(w), where V = V (x) is a vector field, f = f(u) is a scalar function, and A′(·) ≥ 0. The viscous approximate solutions are weak solutions of the initial value problem for the uniformly parabolic equation ∂tw ε + di