A center manifold technique for tracing viscous waves

Stefano Bianchini; Alberto Bressan

doi:10.3934/cpaa.2002.1.161

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2002, Volume 1, Issue 2: 161-190. Doi: 10.3934/cpaa.2002.1.161

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A center manifold technique for tracing viscous waves

Stefano Bianchini^1, and
Alberto Bressan^2,

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

Revised: August 31, 2001

Published: May 2002

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Abstract

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.

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Mathematics Subject Classification: 35L65.

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