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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.08188 |
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| _version_ | 1866917887396020224 |
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| author | Kang, Kyungkeun Kim, Hwa Kil Seo, Geuntaek |
| author_facet | Kang, Kyungkeun Kim, Hwa Kil Seo, Geuntaek |
| contents | We consider a parabolic-elliptic type of Keller-Segel equations with generalized diffusion and logistic source under homogeneous Neumann-Neumann boundary conditions. We construct bounded weak solutions globally in time in an unbalanced optimal transport framework, provided that the magnitude of the chemotactic sensitivity can be restricted depending on parameters. In the case of subquadratic degradation of the logistic source, we quantify the chemotactic sensitivity, in particular, in terms of the power of degradation and the pointwise bound of the initial density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounded weak solutions for Keller-Segel equations with generalized diffusion and logistic source via an unbalanced Optimal Transport splitting scheme Kang, Kyungkeun Kim, Hwa Kil Seo, Geuntaek Analysis of PDEs Optimization and Control We consider a parabolic-elliptic type of Keller-Segel equations with generalized diffusion and logistic source under homogeneous Neumann-Neumann boundary conditions. We construct bounded weak solutions globally in time in an unbalanced optimal transport framework, provided that the magnitude of the chemotactic sensitivity can be restricted depending on parameters. In the case of subquadratic degradation of the logistic source, we quantify the chemotactic sensitivity, in particular, in terms of the power of degradation and the pointwise bound of the initial density. |
| title | Bounded weak solutions for Keller-Segel equations with generalized diffusion and logistic source via an unbalanced Optimal Transport splitting scheme |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2401.08188 |