...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Discrete and continuous dynamical systems >LARGE TIME BEHAVIOR OF EXCHANGE-DRIVEN GROWTH
【24h】

LARGE TIME BEHAVIOR OF EXCHANGE-DRIVEN GROWTH

机译：交换驱动增长的大型时间行为

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Exchange-driven growth (EDG) is a model in which pairs of clusters interact by exchanging single unit with a rate given by a kernel K(j,k). Despite EDG model's common use in the applied sciences, its rigorous mathematical treatment is very recent. In this article we study the large time behaviour of EDG equations. We show two sets of results depending on the properties of the kernel (i) K(j, k) = b_ja_k and (ⅱ) K(j, k) = ja_k + b_j + εβ_jα_k.For type Ⅰ kernels, under the detailed balance assumption, we show that the system admits unique equilibrium up to a critical mass ρ_s above which there is no equilibrium. We prove that if the system has an initial mass below ρ_s then the solutions converge to a unique equilibrium distribution strongly where if the initial mass is above ρ_s then the solutions converge to cricital equilibrium distribution in a weak sense. For type Ⅱ kernels, we do not make any assumption of detailed balance and equilibrium is shown as a consequence of contraction properties of solutions. We provide two separate results depending on the monotonicity of the kernel or smallness of the total mass. For the first case we prove exponential convergence in the number of clusters norm and for the second we prove exponential convergence in the total mass norm.
机译：交换驱动的增长（EDG）是一种模型，其中通过交换单位与由内核K（j，k）给出的速率交换单位的群集。尽管EDG模型在应用的科学中的常见用途，但其严格的数学待遇是最近的。在本文中，我们研究了EDG方程的大时间行为。我们显示两组结果，具体取决于内核（i）k（j，k）= b_ja_k和（Ⅱ）k（j，k）= ja_k + b_j +εβ_jα_k.ForⅠ型内核的属性假设，我们表明该系统承认独特的平衡到高于上面没有平衡的临界质量ρ_。我们证明，如果系统具有低于ρ_的初始质量，则解决方案在初始质量高于ρ_的情况下强烈收敛到独特的平衡分布，然后解决方案在弱道中收敛到危机平衡分布。对于Ⅱ型核，我们不会使任何假设进行详细的平衡和均衡作为解决方案的收缩性能的结果显示。我们提供两个单独的结果，具体取决于内核的单调性或总质量的小。对于第一种情况，我们证明了集群规范数量的指数趋同，并且对于第二种我们证明了总质量范围的指数收敛。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号