A center manifold technique for tracing viscous waves (Q1848476)

This paper is concerned with uniform BV bounds and stability estimates solutions of a special \(2\times 2\) hyperbolic system of conservation laws with viscosity; it is shown that any solution can be locally decomposed as the sum of 2 viscous traveling profiles. An appropriate method based on the center manifold theorem together with a geometric interpretation of the decomposition is given. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data. It is an interesting piece of work that should attract the attention of workers on hyperbolic conservation laws with viscosity.