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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.17241 |
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| _version_ | 1866910787265626112 |
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| author | Hoang, Luan |
| author_facet | Hoang, Luan |
| contents | This paper is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear mapping $A$ and a positively homogeneous scalar function $H$ of a negative degree $-α$. Then any solution with an extinction time $T_*$ behaves like $(T_*-t)^{1/α}ξ_*$ as time $t\to T_*^-$, where $ξ_*$ is an eigenvector of $A$. The result allows the higher order terms to be general and the nonlinear function $H$ to take very complicated forms. As a demonstration, our theoretical study is applied to an inhomogeneous population model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17241 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Behavior near the extinction time for systems of differential equations with sublinear dissipation terms Hoang, Luan Dynamical Systems Classical Analysis and ODEs 34D05, 41A60 This paper is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear mapping $A$ and a positively homogeneous scalar function $H$ of a negative degree $-α$. Then any solution with an extinction time $T_*$ behaves like $(T_*-t)^{1/α}ξ_*$ as time $t\to T_*^-$, where $ξ_*$ is an eigenvector of $A$. The result allows the higher order terms to be general and the nonlinear function $H$ to take very complicated forms. As a demonstration, our theoretical study is applied to an inhomogeneous population model. |
| title | Behavior near the extinction time for systems of differential equations with sublinear dissipation terms |
| topic | Dynamical Systems Classical Analysis and ODEs 34D05, 41A60 |
| url | https://arxiv.org/abs/2211.17241 |