The Burgers-FKPP advection-reaction-diffusion equation with cut-off
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Popovic, Nikola Ptashnyk, Mariya Sattar, Zak |
| author_facet | Popovic, Nikola Ptashnyk, Mariya Sattar, Zak |
| contents | We investigate the effect of a Heaviside cut-off on the front propagation dynamics of the so-called Burgers-FisherKolmogoroff-Petrowskii-Piscounov (Burgers-FKPP) advection-reaction-diffusion equation. We prove the existence and uniqueness of a travelling front solution in the presence of a cut-off in the reaction kinetics and the advection term, and we derive the leading-order asymptotics for the speed of propagation of the front in dependence on the advection strength and the cut-off parameter. Our analysis relies on geometric techniques from dynamical systems theory and specifically, on geometric desingularisation, which also known as blow-up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Burgers-FKPP advection-reaction-diffusion equation with cut-off Popovic, Nikola Ptashnyk, Mariya Sattar, Zak Dynamical Systems We investigate the effect of a Heaviside cut-off on the front propagation dynamics of the so-called Burgers-FisherKolmogoroff-Petrowskii-Piscounov (Burgers-FKPP) advection-reaction-diffusion equation. We prove the existence and uniqueness of a travelling front solution in the presence of a cut-off in the reaction kinetics and the advection term, and we derive the leading-order asymptotics for the speed of propagation of the front in dependence on the advection strength and the cut-off parameter. Our analysis relies on geometric techniques from dynamical systems theory and specifically, on geometric desingularisation, which also known as blow-up. |
| title | The Burgers-FKPP advection-reaction-diffusion equation with cut-off |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.08763 |