Formulation of Chimera Gradient Flows for Chemotaxis Systems with Indirect Signal Production and Degenerate Diffusion
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929392398106624 |
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| author | Mimura, Yoshifumi |
| author_facet | Mimura, Yoshifumi |
| contents | A parabolic system of three unknown functions, not expressible as gradient flows, is treated as three coupled gradient flows. For each unknown function, the minimizing movement scheme is used to construct a time-discrete approximate solution. Unlike standard minimizing movement scheme for gradient flows, the relative compactness of the time-discrete approximate solution with respect to the time step is not inherently guaranteed. However, the existence of a Lyapunov functional ensures this relative compactness, leading to the existence of time-global solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formulation of Chimera Gradient Flows for Chemotaxis Systems with Indirect Signal Production and Degenerate Diffusion Mimura, Yoshifumi Analysis of PDEs A parabolic system of three unknown functions, not expressible as gradient flows, is treated as three coupled gradient flows. For each unknown function, the minimizing movement scheme is used to construct a time-discrete approximate solution. Unlike standard minimizing movement scheme for gradient flows, the relative compactness of the time-discrete approximate solution with respect to the time step is not inherently guaranteed. However, the existence of a Lyapunov functional ensures this relative compactness, leading to the existence of time-global solutions. |
| title | Formulation of Chimera Gradient Flows for Chemotaxis Systems with Indirect Signal Production and Degenerate Diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.14536 |