Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 7, 1617–1859
Issue 6, 1375–1616
Issue 5, 1131–1373
Issue 4, 891–1130
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Stability and instability in scalar balance laws: fronts and periodic waves

Vincent Duchêne and Luis Miguel Rodrigues

Vol. 15 (2022), No. 7, 1807–1859
Abstract

We complete a full classification of nondegenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is the elucidation of the prominent role of characteristic points in the determination of both the spectra of the linearized operators and the phase dynamics involved in the nonlinear large-time evolution. For a generic class of equations an upshot of our analysis is a dramatic reduction from a tremendously wide variety of entropic traveling waves to a relatively small range of stable entropic traveling waves.

Keywords
discontinuous traveling waves, characteristic points, asymptotic stability, scalar balance laws
Mathematical Subject Classification
Primary: 35B35, 35L02, 35L67, 35B40, 35L03
Secondary: 35P15, 37L15
Milestones
Received: 24 June 2020
Revised: 16 December 2020
Accepted: 19 March 2021
Published: 5 December 2022
Authors
Vincent Duchêne
Université de Rennes 1
CNRS, IRMAR, UMR 6625
Rennes
France
Luis Miguel Rodrigues
Université de Rennes 1 and IUF
CNRS, IRMAR, UMR 6625
Rennes
France