Stability in the L1 norm via a linearization method for nonlinear hyperbolic systems
Philippe G. LeFloch
TL;DR
This paper introduces a linearization method to analyze stability in the L1 norm for nonlinear hyperbolic systems, proving continuous dependence of entropy solutions on initial data.
Contribution
It generalizes the Haar method for Glimm-type approximations to establish stability and uniqueness results for nonlinear hyperbolic conservation laws.
Findings
Proves existence and uniqueness of discontinuous solutions
Establishes continuous dependence of solutions on initial data in L1 norm
Extends Haar method to 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.
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Taxonomy
TopicsNavier-Stokes equation solutions · Stability and Controllability of Differential Equations · Advanced Mathematical Physics Problems