Abstract:This paper contains a qualitative study of a scalar conservation law with viscosity:u 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._{t}+f(u)_{x}=u_{xx}.

**Paper:**- Available as PDF (216 Kbytes),
**Author(s):**- W. Shen, <shen_w@math.psu.edu>
- M. Park, <park_m@math.psu.edu>
**Publishing information:**- Submitted to SIAM J. Math. Anal. (2005)
**Comments:**- Revised May 25 2006
**Submitted by:**- <shen_w@math.psu.edu> October 17 2005 and May 26 2006.

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