Stability in the L1 norm via a linearization method for nonlinear hyperbolic systems

2008/12/20 by Philippe G. LeFloch, LeFloch, Philippe G.
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.0812.3999

Abstract

We discuss the existence and uniqueness of discontinuous solutions to adjoint problems associated with nonlinear hyperbolic systems of conservation laws. By generalizing the Haar method for Glimm-type approximations to hyperbolic systems, we establish that entropy solutions depend continuously upon their initial data in the natural L1 norm.

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