Oscillations in a scalar differential equation coupled to a diffusive field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918423881056256 |
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| author | Pelz, Merlin Scheel, Arnd |
| author_facet | Pelz, Merlin Scheel, Arnd |
| contents | We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the diffusive field on boundary kinetics, drawing a parallel to the emergence of oscillations in delay equations. Technically, the Hopf bifurcation occurs in the presence of essential spectrum induced by the diffusive field, preventing a simple approach via center-manifold reduction. The results are motivated by observations in biological systems where dynamic boundary conditions arise when modeling surface dynamics coupled to bulk diffusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Oscillations in a scalar differential equation coupled to a diffusive field Pelz, Merlin Scheel, Arnd Analysis of PDEs Pattern Formation and Solitons 35Bxx We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the diffusive field on boundary kinetics, drawing a parallel to the emergence of oscillations in delay equations. Technically, the Hopf bifurcation occurs in the presence of essential spectrum induced by the diffusive field, preventing a simple approach via center-manifold reduction. The results are motivated by observations in biological systems where dynamic boundary conditions arise when modeling surface dynamics coupled to bulk diffusion. |
| title | Oscillations in a scalar differential equation coupled to a diffusive field |
| topic | Analysis of PDEs Pattern Formation and Solitons 35Bxx |
| url | https://arxiv.org/abs/2604.01135 |