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Stability and
instability in scalar balance laws: fronts and periodic
waves
Vincent Duchêne and Luis Miguel Rodrigues |
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Vol. 15 (2022), No. 7, 1807–1859
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Abstract |
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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. |
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Keywords
discontinuous traveling waves, characteristic points,
asymptotic stability, scalar balance laws
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Mathematical Subject Classification
Primary: 35B35, 35L02, 35L67, 35B40, 35L03
Secondary: 35P15, 37L15
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Milestones
Received: 24 June 2020
Revised: 16 December 2020
Accepted: 19 March 2021
Published: 5 December 2022
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Authors |
| Vincent Duchêne | |
| Université de Rennes 1 CNRS, IRMAR, UMR 6625 Rennes France |
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| Luis Miguel Rodrigues | |
| Université de Rennes 1 and IUF CNRS, IRMAR, UMR 6625 Rennes France |
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