An error estimate for viscous approximate solutions of degenerate parabolic equations

Original · EN

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 ∂ₜ w+div (V(x)f(w))= ΔA(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 ∂ₜ wε+div (V(x) f(wε)) Δ(A(wε)+εwε), ε>0. The error estimate is of order √ε.