On the chain rule formulas for divergences and applications to conservation laws. (April 2017)

• Record Type: Journal Article
• Authors: Crasta, Graziano; De Cicco, Virginia
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 275
• Page End: 293
• Publication Date: 2017-04
• Subjects: 26B30 -- 35L65; Chain rule -- Divergence; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.10.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function v ( x ) = B ( x, u ( x ) ), where B ( ⋅, t ) is a divergence-measure vector field and u is a function of bounded variation. As an application, we prove a uniqueness result for scalar conservation laws with discontinuous flux.