A simple way to well-posedness in $H^{1}$ of a delay differential equation from cell biology
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909220906991616 |
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| author | Aigner, Bernhard Waurick, Marcus |
| author_facet | Aigner, Bernhard Waurick, Marcus |
| contents | We present an application of recent well-posedness results in the theory of delay differential equations for ordinary differential equations arXiv:2308.04730 to a generalized population model for stem cell maturation. The weak approach using Sobolev-spaces we take allows for a larger class of initial prehistories and makes checking the requirements for well-posedness of such a model considerably easier compared to previous approaches. In fact the present approach is a possible means to guarantee that the solution manifold is not empty, which is a necessary requirement for a $C^{1}$-approach to work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06630 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple way to well-posedness in $H^{1}$ of a delay differential equation from cell biology Aigner, Bernhard Waurick, Marcus Analysis of PDEs Populations and Evolution We present an application of recent well-posedness results in the theory of delay differential equations for ordinary differential equations arXiv:2308.04730 to a generalized population model for stem cell maturation. The weak approach using Sobolev-spaces we take allows for a larger class of initial prehistories and makes checking the requirements for well-posedness of such a model considerably easier compared to previous approaches. In fact the present approach is a possible means to guarantee that the solution manifold is not empty, which is a necessary requirement for a $C^{1}$-approach to work. |
| title | A simple way to well-posedness in $H^{1}$ of a delay differential equation from cell biology |
| topic | Analysis of PDEs Populations and Evolution |
| url | https://arxiv.org/abs/2406.06630 |