Asynchronous Exponential Growth of a General Structured Population Model

被引：35

作者：

Banasiak, Jacek ^{[1
,2
]}

Pichor, Katarzyna ^{[3
]}

Rudnicki, Ryszard ^{[3
,4
]}

机构：

[1] Univ KwaZulu Natal, Sch Math Sci, ZA-4041 Durban, South Africa

[2] Tech Univ Lodz, Inst Math, PL-90924 Lodz, Poland

[3] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

[4] Polish Acad Sci, Inst Math, Warsaw, Poland

来源：

ACTA APPLICANDAE MATHEMATICAE | 2012年 / 119卷 / 01期

关键词：

Structured population; Fragmentation equation; First order partial differential equation; Positive semigroups; Asymptotic stability; MARKOV SEMIGROUPS; CELL-GROWTH; STABILITY; DIVISION; EQUATION; DISTRIBUTIONS;

D O I：

10.1007/s10440-011-9666-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of structured cell population models described by a first order partial differential equation perturbed by a general birth operator which describes in a unified way a wide class of birth phenomena ranging from cell division to the McKendrick model. Using the theory of positive stochastic semigroups we establish new criteria for an asynchronous exponential growth of solutions to such equations.

引用

页码：149 / 166

页数：18

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