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On a Lyapunov functional relating shortening curves and viscous conservation laws

TitleOn a Lyapunov functional relating shortening curves and viscous conservation laws
Publication TypeJournal Article
Year of Publication2002
AuthorsBianchini, S, Bressan, A
JournalNonlinear Anal. 51 (2002) 649-662
Abstract

We study a nonlinear 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.

URLhttp://hdl.handle.net/1963/1337
DOI10.1016/S0362-546X(01)00848-3

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