Preprint 1999-030

On a Lyapunov Functional Relating Shortening Curves and Viscous Conservation Laws

Stefano Bianchini and Alberto Bressan

Abstract: 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.

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Stefano Bianchini, <>
Alberto Bressan, <>
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<> October 4 1999.

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