A simple way to well-posedness in H¹ of a delay differential equation from cell biology

2024/06/08 by Bernhard Aigner, Aigner, Bernhard, Marcus Waurick +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.06630

openalex publication_date 2024/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C¹-approach to work.

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