An error estimate for viscous approximate solutions of degenerate parabolic equations

Details An error estimate for viscous approximate solutions of degenerate parabolic equations An error estimate for viscous approximate solutions of degenerate parabolic equations

2003-02-04

arxiv.org/abs/math/0302038v1

J. Nonlinear Math. Phys., volume 9, no. 3 (2002) 262-281

Mathematics

Analysis of PDEs

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Scientific paper

Relying on recent advances in the theory of entropy solutions for nonlinear (strongly) degenerate parabolic equations, we present a direct proof of an L^1 error estimate for viscous approximate solutions of the initial value problem for \partial_t w+\mathrm{div} \bigl(V(x)f(w)\bigr)= \Delta A(w) where V=V(x) is a vector field, f=f(u) is a scalar function, and A'(.) \geq 0. The viscous approximate solutions are weak solutions of the initial value problem for the uniformly parabolic equation \partial_t w^{\epsilon}+\mathrm{div} \bigl(V(x) f(w^{\epsilon})\bigr) \Delta \bigl(A(w^{\epsilon})+\epsilon w^{\epsilon}\bigr), \epsilon>0. The error estimate is of order \sqrt{\epsilon}.

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