Work

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

Year: 2025

Type: article

Abstract: We present an application of recent well-posedness results in the theory of delay differential equations for ordinary differential equations [10] 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.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113241

Authors: Bernhard Aigner, Marcus Waurick

Institution: TU Bergakademie Freiberg

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Freistaat Sachsen