Extinction of multiple shocks in the modular Burgers equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913513182593024 |
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| author | Pelinovsky, Dmitry E. de Rijk, Bjorn |
| author_facet | Pelinovsky, Dmitry E. de Rijk, Bjorn |
| contents | We consider multiple shock waves in the Burgers' equation with a modular advection term. It was previously shown that the modular Burgers' equation admits a traveling viscous shock with a single interface, which is stable against smooth and exponentially localized perturbations. In contrast, we suggest in the present work with the help of energy estimates and numerical simulations that the evolution of shock waves with multiple interfaces leads to finite-time coalescence of two consecutive interfaces. We formulate a precise scaling law of the finite-time extinction supported by the interface equations and by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_06467 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extinction of multiple shocks in the modular Burgers equation Pelinovsky, Dmitry E. de Rijk, Bjorn Analysis of PDEs Dynamical Systems Pattern Formation and Solitons We consider multiple shock waves in the Burgers' equation with a modular advection term. It was previously shown that the modular Burgers' equation admits a traveling viscous shock with a single interface, which is stable against smooth and exponentially localized perturbations. In contrast, we suggest in the present work with the help of energy estimates and numerical simulations that the evolution of shock waves with multiple interfaces leads to finite-time coalescence of two consecutive interfaces. We formulate a precise scaling law of the finite-time extinction supported by the interface equations and by numerical simulations. |
| title | Extinction of multiple shocks in the modular Burgers equation |
| topic | Analysis of PDEs Dynamical Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2205.06467 |