Asymptotic stabilization of stationnary shock waves using a boundary feedback law
Vincent Perrollaz (LMPT)
TL;DR
This paper introduces a boundary feedback law for scalar conservation laws with convex flux, ensuring asymptotic stability of stationary shock waves in the L1-norm within the entropy solution class.
Contribution
It presents a novel boundary feedback law that stabilizes stationary shock waves asymptotically, expanding control methods for scalar conservation laws.
Findings
Stationary shock waves can be stabilized using the proposed boundary feedback law.
The stabilization is achieved in the L1-norm within the entropy solution framework.
The method provides a new approach to controlling scalar conservation laws with convex flux.
Abstract
In this paper we consider scalar conservation laws with a convex flux. Given a stationnary shock, we provide a feedback law acting at one boundary point such that this solution is now asymptotically stable in L 1-norm in the class of entropy solution.
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Taxonomy
TopicsComputational Fluid Dynamics and Aerodynamics · Navier-Stokes equation solutions · Fluid Dynamics and Turbulent Flows