Decay with a Rate for Noncompactly Supported Solutions of Conservation Laws

摘要

This document shows that solutions of the Cauchy problem for systems of two conservation laws decay in the supnorm at a rate that depends only on the L sub 1 norm of the initial data. This implies that the dissipation due to the entropy dominates the nonlinearities in the problem at a rate depending only on the L sub 1 norm of the initial data. The main estimate requires an analysis of approximate characteristics for its proof. A general framework is developed for the study of approximate characteristics, and the main estimate is obtained for an arbitrary number of equations.