Persistence of generalized roll-waves under viscous perturbation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1286.35164
DOI: 10.1137/100789798
author: Valérie Le Blanc
published in: SIAM Journal on Mathematical Analysis
publication date: 2013-07-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.3459
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 6189155
zbMATH Keywords: large shocks
zbMATH Keywords: Green's function
zbMATH Keywords: conservation law with source
zbMATH Keywords: spatially periodic solutions
MaRDI profile type: Publication
OpenAlex ID: W2951574131
arXiv ID: 1004.3459
Recommended article: Non-persistence of roll-waves under viscous perturbations
Recommended article: Persistence of Roll Waves for the Saint Venant Equations
Recommended article: Nonlinear Stability of Viscous Roll Waves
Recommended article: Linear Stability of Viscous Roll Waves
Recommended article: Q5394895
Recommended article: Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit
Recommended article: Roll waves on a shallow layer of a dilatant fluid
Recommended article: On the linear stability of Roll-Waves
Recommended article: Periodic-Coefficient Damping Estimates, and Stability of Large-Amplitude Roll Waves in Inclined Thin Film Flow
Recommended article: Spectral stability of inviscid roll waves
title: Persistence of generalized roll-waves under viscous perturbation
review text: The author studies spatially periodic solutions of a hyperbolic conservation law \(u_t+f(u)_x=g(u)\) with a linear source under small viscous perturbations \(\varepsilon u_{xx}\). She is interested in the persistence of so-called roll waves, which are solutions with several shock waves of arbitrary strength. Under the assumption that the shocks remain non-interacting and possess a viscous profile which is linearly stable, she constructs an approximate solution up to second order and derives error estimates for the Green's function of the linearized operator around this approximate solution. To this end a careful splitting into nine different Green's kernels is necessary which describe the different wave productions and interactions near the shocks. Using these estimates existence of a solution to the original problem can be shown.
reviewed by: Jörg Härterich
description: scientific article; zbMATH DE number 6189155