Convective stability in scalar balance laws
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910398498734080 |
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| author | Garénaux, Louis Rodrigues, L. Miguel |
| author_facet | Garénaux, Louis Rodrigues, L. Miguel |
| contents | We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we investigate the impact on the classification of allowing to restrict perturbations by further localization constraints, the so-called convective stability analysis. On the other hand, in the multidimensional case we extend the existing analysis to general perturbations, relaxing the artificial restriction, assumed so far, that initial perturbations are supported away from characteristic points. A striking feature of the latter analysis is that it involves infinite-dimensional families of genuinely multidimensional traveling waves that live near the perturbed planar traveling wave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convective stability in scalar balance laws Garénaux, Louis Rodrigues, L. Miguel Analysis of PDEs Dynamical Systems 35B35 (Primary), 35L02, 35L67, 35B40, 35L03, 35P15, 37L15 (Secondary) We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we investigate the impact on the classification of allowing to restrict perturbations by further localization constraints, the so-called convective stability analysis. On the other hand, in the multidimensional case we extend the existing analysis to general perturbations, relaxing the artificial restriction, assumed so far, that initial perturbations are supported away from characteristic points. A striking feature of the latter analysis is that it involves infinite-dimensional families of genuinely multidimensional traveling waves that live near the perturbed planar traveling wave. |
| title | Convective stability in scalar balance laws |
| topic | Analysis of PDEs Dynamical Systems 35B35 (Primary), 35L02, 35L67, 35B40, 35L03, 35P15, 37L15 (Secondary) |
| url | https://arxiv.org/abs/2401.06677 |