Volume 9, Issue 3, August 2002, Pages 261 - 281
An Error Estimate for Viscous Approximate Solutions of Degenerate Parabolic Equations
Authors
Steinar Evje, Kenneth H. Karlsen
Corresponding Author
Steinar Evje
Received 14 February 2001, Revised 13 December 2001, Accepted 13 February 2002, Available Online 1 August 2002.
- DOI
- 10.2991/jnmp.2002.9.3.3How to use a DOI?
- 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 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 + div V (x)f(w ) = A(w ) + w , > 0. The error estimate is of order
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Steinar Evje AU - Kenneth H. Karlsen PY - 2002 DA - 2002/08/01 TI - An Error Estimate for Viscous Approximate Solutions of Degenerate Parabolic Equations JO - Journal of Nonlinear Mathematical Physics SP - 261 EP - 281 VL - 9 IS - 3 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.3.3 DO - 10.2991/jnmp.2002.9.3.3 ID - Evje2002 ER -