On the Homogenization of the Renewal Equation with Heterogeneous External Constraints

被引：0
作者：
Étienne Bernard
Francesco Salvarani
机构：
[1] CERMICS,Dipartimento di Matematica “F. Casorati”
[2] École des Ponts ParisTech,undefined
[3] Léonard de Vinci Pôle Universitaire,undefined
[4] Università degli Studi di Pavia,undefined
来源：
Acta Applicandae Mathematicae | 2023年 / 187卷
关键词：
Renewal equation; Homogenization; Two-scale convergence; 35B27; 35Q92;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.
引用
收藏
相关论文
共 26 条
[1]  
Allaire G.(1992)Homogenization and two-scale convergence SIAM J. Math. Anal. 23 1482-1518
[2]  
Amirat Y.(1989)Homogénéisation d’équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux Ann. Inst. Henri Poincaré, Anal. Non Linéaire 6 397-417
[3]  
Hamdache K.(2000)Homogenization of transport equations SIAM J. Appl. Math. 60 1447-1470
[4]  
Ziani A.(1992)Homogenization of linear and nonlinear transport equations Commun. Pure Appl. Math. 45 301-326
[5]  
Dumas L.(1903)The effect of low temperature upon bacterial life J. State Med. (1892-1905) 11 43-45
[6]  
Golse F.(1992)Homogenization of linear transport equations with oscillatory vector fields SIAM J. Appl. Math. 52 34-45
[7]  
E W.(2020)Homogenization in the energy variable for a neutron transport model Asymptot. Anal. 117 1-25
[8]  
Hewlett R.T.(2006)Two-sclae homogenization and memory effects of a first order differential equation Taiwan. J. Math. 10 963-976
[9]  
Hou T.(1925)Applications of mathematics to medical problems Proc. Edinb. Math. Soc. 44 98-130
[10]  
Xin X.(1949)The growth of bacterial cultures Annu. Rev. Microbiol. 3 371-394
123