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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.16300 |
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| _version_ | 1866908666950582272 |
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| author | Qin, Qian Jiao, JinJing Wang, Zhiguo Nie, Hua |
| author_facet | Qin, Qian Jiao, JinJing Wang, Zhiguo Nie, Hua |
| contents | This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of the system, showing that it follows a spreading-vanishing dichotomy: the two species either spread across the entire region or eventually die out. In the case of spreading, we determine the asymptotic spreading speed of the fronts by using a semi-wave system and provide sharp estimates for the moving fronts. Additionally, we show that the solution to the system converges to the corresponding semi-wave solution as time tends to infinity. These results contribute to a deeper understanding of the long-term dynamics of cooperative species in reaction-diffusion systems with free boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior and sharp estimates for spreading fronts in a cooperative system with free boundaries Qin, Qian Jiao, JinJing Wang, Zhiguo Nie, Hua Analysis of PDEs This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of the system, showing that it follows a spreading-vanishing dichotomy: the two species either spread across the entire region or eventually die out. In the case of spreading, we determine the asymptotic spreading speed of the fronts by using a semi-wave system and provide sharp estimates for the moving fronts. Additionally, we show that the solution to the system converges to the corresponding semi-wave solution as time tends to infinity. These results contribute to a deeper understanding of the long-term dynamics of cooperative species in reaction-diffusion systems with free boundaries. |
| title | Asymptotic behavior and sharp estimates for spreading fronts in a cooperative system with free boundaries |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.16300 |