%0 Journal Article
%J Comm. Pure Appl. Math. 57 (2004) 1075-1109
%D 2004
%T On the convergence rate of vanishing viscosity approximations
%A Alberto Bressan
%A Tong Yang
%X Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.
%B Comm. Pure Appl. Math. 57 (2004) 1075-1109
%I Wiley
%G en_US
%U http://hdl.handle.net/1963/2915
%1 1785
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:30:25Z\\nNo. of bitstreams: 1\\nmath.AP0307141.pdf: 265243 bytes, checksum: 795adebd067228364ac1240add5f7b02 (MD5)
%R 10.1002/cpa.20030