Decay with a Rate for Noncompactly Supported Solutions of Conservation Laws.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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. Keywords Riemann Problem Random Choice Method Decay Stability Continuous Dependence Conservation Laws nonlinear partial differential equations.
- Numerical Mathematics