基于细胞分子含量分层的群体模型分析
Analysis of a Population Model Structured by the Cells Molecular Content
AI总结：
研究具有多个内部变量的细胞分裂模型的数学性质，通过正则化技术解决出生项退化问题，证明长时间收敛并推广到非线性问题。
摘要：
我们研究了一个具有多个内部变量的细胞分裂一般模型的数学性质。首先从一个更简单的两个变量的具体模型开始，在强或弱假设下求解特征值问题，并由此推导出长时间收敛。主要困难来自出生项的自然退化，我们通过正则化技术克服了这一困难。然后我们将结果推广到多个参数的情形，并回顾该简化模型与文献\cite{CBBP1}中模型之间的联系；还给出了非线性问题的应用，导致总群体的稳健次多项式增长。
英文摘要：
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this simplified model and the one presented in \cite{CBBP1}; an application to the non-linear problem is also given, leading to robust subpolynomial growth of the total population.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
