Preprint 2004-025

Burgers' Equation with Vanishing Hyper-Viscosity

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.