An error estimate for viscous approximate solutions of degenerate parabolic equations

2003/02/04 by Steinar Evje, Kenneth H. Karlsen · 1 citation
Mathematics · #math.AP

paper · pdf

published as J. Nonlinear Math. Phys., volume 9, no. 3 (2002) 262-281 · arxiv version is already official

arxiv created 2003/02/04 · arxiv updated 2009/11/30

Abstract

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 w^ε+div (V(x) f(w^ε)) Δ(A(w^ε)+εw^ε), ε>0. The error estimate is of order √ε.

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