2016/05/29 by Graziano Crasta, Virginia De Cicco
Mathematics · #Bounded function #Bounded variation #Chain (unit) #Combinatorics #Conservation law #Divergence (linguistics) #Function (biology) #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Scalar field #Uniqueness #Vector-valued function #math.AP
paper · pdf · doi:10.1016/j.na.2016.10.005
published as Nonlinear Analysis: Theory, Methods & Applications 153 (2017), Pages 275-293 · 19 pages
arxiv created 2016/05/29 · openalex created_date 2016/06/24 · openalex publication_date 2016/10/24 · arxiv updated 2019/05/24 · openalex updated_date 2026/08/05
In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function \boldsymbolv(x)=\boldsymbolB(x,u(x)), where \boldsymbolB(⋅,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.