%0 Journal Article
%J Ann. of Math. 161 (2005) 223-342
%D 2005
%T Vanishing viscosity solutions of nonlinear hyperbolic systems
%A Stefano Bianchini
%A Alberto Bressan
%X We consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$.
%B Ann. of Math. 161 (2005) 223-342
%I Annals of Mathematics
%G en_US
%U http://hdl.handle.net/1963/3074
%1 1259
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:46:16Z\\nNo. of bitstreams: 1\\n0111321v1.pdf: 746310 bytes, checksum: f3b7c9e76e33050e9f367ba2c57e2161 (MD5)
%0 Journal Article
%D 1999
%T Vanishing viscosity solutions of hyperbolic systems on manifolds
%A Stefano Bianchini
%A Alberto Bressan
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/1238
%1 2705
%2 Mathematics
%3 Functional Analysis and Applications
%$ Made available in DSpace on 2004-09-01T12:55:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999