# American Institute of Mathematical Sciences

June  2002, 1(2): 161-190. doi: 10.3934/cpaa.2002.1.161

## A center manifold technique for tracing viscous waves

 1 IAC-CNR, viale del Policlinico 137, 00161 ROMA 2 S.I.S.S.A., Via Beirut, 2-4, 34014 Trieste, Italy

Revised  September 2001 Published  March 2002

In this paper we introduce a new technique for tracing viscous travlling profiles. To illustrate the method, we consider a special $2\times 2$ hyperbolic system of conversation laws with viscosity, and show that any solution can be locally decomposed as the sume of 2 viscous travlling proflies. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.
Citation: Stefano Bianchini, Alberto Bressan. A center manifold technique for tracing viscous waves. Communications on Pure & Applied Analysis, 2002, 1 (2) : 161-190. doi: 10.3934/cpaa.2002.1.161
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