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

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.

15 pages

References in corpus (2)

• Why many theories of shock waves are necessary. Convergence error in formally path-consistent schemes
• Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions