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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12660 |
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| _version_ | 1866914649232900096 |
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| author | Gauss, Nicole Logioti, Anna Schneider, Guido Zimmermann, Dominik |
| author_facet | Gauss, Nicole Logioti, Anna Schneider, Guido Zimmermann, Dominik |
| contents | We are interested in reaction-diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number $k = 0$. With the help of a multiple scaling perturbation ansatz a Ginzburg-Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction-diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence for long wave Hopf unstable spatially extended systems with a conservation law Gauss, Nicole Logioti, Anna Schneider, Guido Zimmermann, Dominik Analysis of PDEs Dynamical Systems We are interested in reaction-diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number $k = 0$. With the help of a multiple scaling perturbation ansatz a Ginzburg-Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction-diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions. |
| title | Global existence for long wave Hopf unstable spatially extended systems with a conservation law |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2401.12660 |