Work

Sharp a-contraction estimates for small extremal shocks

Year: 2023

Type: article

Abstract: In this paper, we study the [Formula: see text]-contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected to large perturbations. We show that the weight coefficient [Formula: see text] can be chosen with amplitude proportional to the size of the shock. The main result of this paper is a key building block in the companion paper [G. Chen, S. G. Krupa and A. F. Vasseur, Uniqueness and weak-BV stability for [Formula: see text] conservation laws, Arch. Ration. Mech. Anal. 246(1) (2022) 299–332] in which uniqueness and BV-weak stability results for [Formula: see text] systems of hyperbolic conservation laws are proved.

Source: Journal of Hyperbolic Differential Equations

DOI: 10.1142/s0219891623500170

Authors: William M. Golding, Sam G. Krupa, Alexis F. Vasseur

Institutions: The University of Texas at Austin, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: RTG: Analysis of Partial Differential Equations, Stability of shocks and layers in Fluid Mechanics and related problems