On the Piecewisely Smooth Solutions to Non-homogeneous Scalar Conservation
Y.-X. Kan, T. Tang, and Z.-H. Teng
We study the structure and smoothness of non-homogeneous convex conservation
laws. The question regarding the number of smoothness pieces is addressed.
It is shown that under certain conditions on the initial data the entropy
solution has only finite number of discontinuous curves. We also obtain some
global estimates on derivatives of the piecewisely smooth entropy solution
along the generalized characteristics. These estimates play important roles
in obtaining the optimal rate of convergence for various approximation methods
to conservation laws.
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- Y.-X. Kan
- T. Tang,
- Z.-H. Teng,
- Publishing information:
- To appear in J. Diff. Equations
- Submitted by:
May 8 2001.
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