A center manifold technique for tracing viscous waves

Stefano Bianchini, and Alberto Bressan
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Submission date: 25. Sep. 2001
Pages: 27
published in: Communications on pure and applied analysis, 1 (2002) 2, p. 161-190 
MSC-Numbers: 35L65
Keywords and phrases: hyperbolic systems, conservation laws, well posedness
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Abstract:
In this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.