Structure and regularity of solutions to 1d scalar conservation laws

2019/06/12 by Elio Marconi, Marconi, Elio
Mathematics · Physics and Astronomy · Engineering · #Navier-Stokes equation solutions #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1906.05003

Abstract

We consider bounded entropy solutions to the scalar conservation law in one space dimension: u_t+f(u)_x=0. We quantify the regularizing effect of the non linearity of the flux f on the solution u in terms of spaces of functions with bounded generalized variation.

Related

• Structure of entropy solutions to general scalar conservation laws in one space dimension
• Non existence of the BV regularizing effect for scalar conservation laws in several space dimension
• L¹-Contraction Property of Entropy Solutions for Scalar Conservation Laws with Minimal Regularity Assumptions on the Flux
• Fractional regularity for conservation laws with discontinuous flux
• Regularity of solutions to scalar conservation laws with a force