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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/2504.01765 |
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| _version_ | 1866916672024084480 |
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| author | Rakotomalala, Matthias de Wit, Oscar |
| author_facet | Rakotomalala, Matthias de Wit, Oscar |
| contents | We study the asymptotic behavior of a nonlinear PDE model for ant trail formation, which was introduced in [3]. We establish the existence of a compact global attractor and prove the nonlinear instability of the homogeneous steady state under an inviscid instability condition. We also provide a dimensional lower bound on the attractor. Alternatively, we prove that if the interaction parameter is sufficiently small, the homogeneous steady state is globally asymptotically stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and dimensional lower bound for the global attractor of a PDE model for ant trail formation Rakotomalala, Matthias de Wit, Oscar Analysis of PDEs We study the asymptotic behavior of a nonlinear PDE model for ant trail formation, which was introduced in [3]. We establish the existence of a compact global attractor and prove the nonlinear instability of the homogeneous steady state under an inviscid instability condition. We also provide a dimensional lower bound on the attractor. Alternatively, we prove that if the interaction parameter is sufficiently small, the homogeneous steady state is globally asymptotically stable. |
| title | Existence and dimensional lower bound for the global attractor of a PDE model for ant trail formation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.01765 |