On a Lyapunov Functional Relating Shortening Curves and Viscous
Stefano Bianchini and Alberto Bressan
We study a non linear functional which controls the area
swept by a curve moving in the plane in the direction of curvature.
In turn, this yields a priori estimates on solutions to a class of
parabolic equations and of scalar viscous conservation laws.
A further application provides an estimate on the
``change of shape'' of a BV solution to a
scalar conservation law.
- Available as PostScript.
- Stefano Bianchini,
- Alberto Bressan,
- Publishing information:
- Submitted by:
October 4 1999.
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Last modified: Mon Oct 4 16:31:03 1999