Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

Abstract

In this paper, we study systems of conservation laws in one space dimension. We prove that for classical solutions in Sobolev spaces

H^s

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^s$$\end{document}

, with s > 3/2, the data-to-solution map is not uniformly continuous. Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.

Keywords

Conservation laws / Data-to-solution map / Nonuniform dependence

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