Stability and instability in scalar balance laws: fronts and periodic waves
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866929485182402560 |
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| author | Duchêne, Vincent Rodrigues, Luis Miguel |
| author_facet | Duchêne, Vincent Rodrigues, Luis Miguel |
| contents | We complete a full classification of non-degenerate 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2006_14236 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Stability and instability in scalar balance laws: fronts and periodic waves Duchêne, Vincent Rodrigues, Luis Miguel Analysis of PDEs 35B35, 35L02, 35L67, 35B40, 35L03, 35P15, 37L15 We complete a full classification of non-degenerate 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. |
| title | Stability and instability in scalar balance laws: fronts and periodic waves |
| topic | Analysis of PDEs 35B35, 35L02, 35L67, 35B40, 35L03, 35P15, 37L15 |
| url | https://arxiv.org/abs/2006.14236 |