Preprint 2005-039

Optimal Tracing of Viscous Shocks in Solutions of Viscous Conservation Laws

W. Shen and M. Park

Abstract: This paper contains a qualitative study of a scalar conservation law with viscosity:

We consider the problem of identifying the location of viscous shocks, thus obtaining an optimal finite dimensional description of solutions to the viscous conservation law. We introduce a nonlinear functional whose minimizers yield the viscous travelling profiles which ``optimally fit'' the given solution. We prove that, outside an initial time interval and away from times of shock interactions, our functional remains very small, i.e.~the solution can be accurately represented by a finite number of viscous travelling waves.

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W. Shen, <>
M. Park, <>
Publishing information:
Submitted to SIAM J. Math. Anal. (2005)
Revised May 25 2006
Submitted by:
<> October 17 2005 and May 26 2006.

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