On the inverse problem for a size-structured population model
On the inverse problem for a size-structured population model
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DOI：
10.1088/0266-5611/23/3/012
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发表时间：
2007-06-01
期刊：
影响因子：
2.1
通讯作者：
Zubelli, Jorge P.
中科院分区：
文献类型：
--
作者：
Perthame, Benoit;Zubelli, Jorge P.
我们考虑了一个细胞分裂的大小结构模型，并解决了从测量的稳定的种群大小分布确定分裂（出生）率的问题。我们将这个问题表述为半直线上的积分-微分方程的反问题。我们首先发展了一个关于系数的正则相关解的理论，其次，考虑到方程的特殊性，我们提出了一种新的正则化技术来解决这个逆问题。我们的结果也依赖于广义相对熵估计和相关的庞加莱不等式。
We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We formulate such a question as an inverse problem for an integro-differential equation posed on the half line. We develop firstly a regular dependence theory for the solution in terms of the coefficients and, secondly, a novel regularization technique for tackling this inverse problem which takes into account the specific nature of the equation. Our results also rely on generalized relative entropy estimates and related Poincare inequalities.