TIME ASYMPTOTICS FOR A CRITICAL CASE IN FRAGMENTATION AND GROWTH-FRAGMENTATION EQUATIONS
TIME ASYMPTOTICS FOR A CRITICAL CASE IN FRAGMENTATION AND GROWTH-FRAGMENTATION EQUATIONS
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DOI：
10.3934/krm.2016.9.251
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发表时间：
2016-06-01
影响因子：
1
通讯作者：
Escobedo, Miguel
中科院分区：
文献类型：
--
作者：
Doumic, Marie;Escobedo, Miguel
碎裂和增长碎裂方程是一类应用广泛的问题。本文讨论了当分裂率为常数，增长率为线性或零时，这类方程的两种临界情形的长时间渐近性。对这些情形的研究可以归结为对以下碎裂方程的研究：偏导数/偏导数tu（t，x）+ u（t，x）= integral（infinity）（x）k（0）（x/y）u（t，y）dy.利用方程的Mellin变换，我们确定了解的长时间行为.我们的研究结果表明，特别是强的依赖性，这种渐近行为相对于初始数据。
Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, when the division rate is constant and the growth rate is linear or zero. The study of these cases may be reduced to the study of the following fragmentation equation:partial derivative/partial derivative tu(t, x) + u(t, x) = integral(infinity)(x) k(0) (x/y)u(t, y)dy.Using the Mellin transform of the equation, we determine the long-time behavior of the solutions. Our results show in particular the strong dependence of this asymptotic behavior with respect to the initial data.