$L^2$-type Lyapunov functions for hyperbolic scalar conservation laws
Denis Serre (UMPA-ENSL)
TL;DR
This paper proves that solutions to hyperbolic scalar conservation laws decay in L2-distance to certain convex, flow-invariant sets, providing insights into their long-term behavior.
Contribution
It introduces L2-type Lyapunov functions to analyze the decay properties of solutions to hyperbolic scalar conservation laws.
Findings
Solutions decay in L2-distance over time
Decay occurs towards convex, flow-invariant sets
Provides a new Lyapunov function framework
Abstract
We prove the decay of the L 2-distance from the solution u(t) of a hyperbolic scalar conservation law, to some convex, flow-invariant target sets.
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Taxonomy
TopicsNavier-Stokes equation solutions · Advanced Mathematical Physics Problems · Geometric Analysis and Curvature Flows