Quadratic Growth Model with Discontinuity: A Link between Monostable and Bistable Traveling Waves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908514640723968 |
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| author | Choi, Wonhyung Bae, Junsik Kim, Yong-Jung |
| author_facet | Choi, Wonhyung Bae, Junsik Kim, Yong-Jung |
| contents | We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures finite-time extinction for sub-threshold populations. This discontinuity induces a free boundary in the wave profile, a phenomenon that distinguishes the model from the classical logistic or Allen-Cahn equations. A complete scenario is presented that connects monostable and bistable traveling waves through the wave speed parameter, thereby providing a unified framework for their dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic Growth Model with Discontinuity: A Link between Monostable and Bistable Traveling Waves Choi, Wonhyung Bae, Junsik Kim, Yong-Jung Analysis of PDEs Classical Analysis and ODEs We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures finite-time extinction for sub-threshold populations. This discontinuity induces a free boundary in the wave profile, a phenomenon that distinguishes the model from the classical logistic or Allen-Cahn equations. A complete scenario is presented that connects monostable and bistable traveling waves through the wave speed parameter, thereby providing a unified framework for their dynamics. |
| title | Quadratic Growth Model with Discontinuity: A Link between Monostable and Bistable Traveling Waves |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.01715 |