Structure and regularity of solutions to 1d scalar conservation laws

Abstract

We consider bounded entropy solutions to the scalar conservation law in one space dimension: \begin{equation*} u_t+f(u)_x=0. \end{equation*} 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.

References in corpus (1)

• Quadratic interaction functional for general systems of conservation laws

Cited by in corpus (1)

• Optimal regularity for all time for entropy solutions of conservation laws in $B{V}^s$