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

IF 2.4 2区 数学 Q1 MATHEMATICS
Bernhard Aigner , Marcus Waurick
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引用次数: 0

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 C1-approach to work.
我们介绍了最近在常微分方程延迟微分方程理论[10]中的拟合结果在干细胞成熟的广义群体模型中的应用。我们采用的使用索博廖夫空间的弱方法允许更多类型的初始预史,并且与以前的方法相比,更容易检查这种模型的摆好性要求。事实上,本方法是保证解流形不为空的一种可行方法,而这正是 C1 方法发挥作用的必要条件。
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
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