关于离散凝聚-湮灭系统的适定性与长时间动力学

中文摘要 AI 辅助

本文研究了由E. Ben-Naim和P. Krapivsky在《物理评论E》（1995年）中首次提出的离散凝聚-湮灭模型的适定性。我们首先针对一大类凝聚和湮灭速率（包括可能无界的速率）建立了解的存在性。这些结果通过将一致估计与Helly选择定理及Rellich-Kondrachov紧嵌入定理相结合而获得。在这些速率的适当结构假设下，我们进一步证明了解对初始数据的唯一性和连续依赖性，从而确立了模型的适定性。最后，对于特定类别的凝聚和湮灭速率，我们还研究了解的可微性并刻画了其长时间渐近行为。这些结果为该模型的分析提供了严格的数学框架，并有助于更深入地理解其适定性、正则性和长时间动力学。

英文摘要

The present article investigates the well--posedness of a discrete coagulation--annihilation model originally introduced by E. Ben-Naim and P. Krapivsky in Physical Review E (1995). We first establish the existence of solutions for a broad class of coagulation and annihilation rates, including rates that may be unbounded. These results are obtained by combining uniform estimates with Helly's selection theorem and the Rellich--Kondrachov compact embedding theorem. Under appropriate structural assumptions on these rates, we further prove uniqueness and continuous dependence of solutions on the initial data, thereby establishing well--posedness of the model. Finally, for a specific class of coagulation and annihilation rates, we additionally study the differentiability of solutions and characterize their long--time asymptotic behaviour. These results provide a rigorous mathematical framework for the analysis of the model and contribute to a deeper understanding of its well--posedness, regularity, and long-time dynamics.

发表机构

• Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校）
• University of Pretoria（比勒陀利亚大学）

机构由 AI 辅助整理，请以论文原文为准。