Mathematical analysis of an abstract model and its applications to structured populations (I)

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2022021

M. Boulanouar

引用次数: 0

Abstract

The first part of this works deals with an integro–differential operator with boundary condition related to the interior solution. We prove that the model is governed by a strongly continuous semigroup and we precise its growth inequality. In the second part of this works, we model the proliferation-quiescence phases through a system of first order equations. We also prove that the proliferation-quiescence model is governed by a strongly continuous semigroup and we precise its growth inequality. In the last part, we give some applications in Demography and Biology.

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抽象模型的数学分析及其在结构种群中的应用(I)

本文的第一部分讨论了一个与内解有关的边界条件的积分微分算子。证明了该模型是由一个强连续半群控制的，并精确了它的生长不等式。在本文的第二部分，我们通过一个一阶方程组来模拟扩散-静止阶段。我们还证明了增殖-静止模型是由一个强连续半群控制的，并精确了它的生长不等式。最后，给出了在人口统计学和生物学中的一些应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology