Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913233931075584 |
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| author | Holzer, Matt Kearney, Matthew Molseed, Samuel Tuttle, Katie Wigginton, David |
| author_facet | Holzer, Matt Kearney, Matthew Molseed, Samuel Tuttle, Katie Wigginton, David |
| contents | We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine the leading order expansion for the selected wavespeed. Such fronts are often constructed as transverse intersections of stable and unstable manifolds of the traveling wave differential equation. However, a re-scaling of the dependent variable leads to a lack of hyperbolicity for one of the end states making the definition of one such manifold unclear. We use geometric blow-up techniques to recover hyperbolicity and following an analysis of the blown up vector field are able to show the existence of a traveling front with a leading order expansion of its speed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06724 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization Holzer, Matt Kearney, Matthew Molseed, Samuel Tuttle, Katie Wigginton, David Analysis of PDEs Dynamical Systems We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine the leading order expansion for the selected wavespeed. Such fronts are often constructed as transverse intersections of stable and unstable manifolds of the traveling wave differential equation. However, a re-scaling of the dependent variable leads to a lack of hyperbolicity for one of the end states making the definition of one such manifold unclear. We use geometric blow-up techniques to recover hyperbolicity and following an analysis of the blown up vector field are able to show the existence of a traveling front with a leading order expansion of its speed. |
| title | Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2212.06724 |