Abstract:We prove that bounded solutions of the vanishing hyper-viscosity equation, $u_t+f(u)_x+(-1)^{s}\eps\partial^{2s}_x u=0$ converge to the entropy solution of the corresponding convex conservation law $u_t+f(u)_x=0, \ f'' >0$. The hyper-viscosity case, $s>1$, lacks the monotonicity which underlines the Krushkov BV theory in the viscous case $s=1$. Instead we show how to adapt the Tartar-Murat compensated compactness theory together with a weaker entropy dissipation bound to conclude the convergence of the vanishing hyper-viscosity.

**Paper:**- Available as PDF (125 Kbytes).
**Author(s):**- Eitan Tadmor, <tadmor@cscamm.umd.edu>
**Publishing information:**- Communications in Math. Sciences 2 (2), (2004) To appear.
**Comments:****Submitted by:**- <tadmor@cscamm.umd.edu> May 24 2004.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | All Preprints | Preprint Server Homepage ]

Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Tue May 25 10:04:17 MEST 2004