具退化扩散与非局部性聚集的Keller-Segel方程

发布时间：2018-02-01 09:07

本文关键词： Keller-Segel模型退化扩散非局部聚集整体存在爆破弱解唯一性　出处：《大连理工大学》2016年博士论文　论文类型：学位论文

【摘要】：本文考虑如下具有退化扩散与非局部聚集的Keller-Segel方程本文研究模型解的性态,包括弱解的整体存在与唯一性,以及弱解的有限时刻b1ow-up.全文分以下五个章节：第一章简述模型的背景及研究现状.第二章讨论在一般条件下模型解的性态.证明了对存在常数Cdm0,使得如果初值么弱解整体存在；如果初始自由能泛函满足F[u0]0(蕴含那么弱解有限时刻blow-up.此外,还得到整体弱解的衰减估计.第三章限制在指标范围进一步讨论解的整体存在性与有限时刻blow-up,在该指标范围建立区分解整体存在与有限时刻blow-up的最佳临界.最佳临界的证明依赖于自由能泛函与HLS不等式之间的关系.第四章讨论弱解的唯一性,利用最优传输方法,得到在Wasserstein距离意义下整体弱熵解的稳定性与唯一性.第五章给出本文主要结果的总结以及未来工作的展望.
[Abstract]:In this paper, we consider the following Keller-Segel equations with degenerate diffusion and nonlocal aggregation. In this paper, we study the global existence and uniqueness of the solution of the model, including the global existence and uniqueness of the weak solution. And the finite moment b1ow-up. this paper is divided into five chapters:. In chapter 1, the background and research status of the model are briefly introduced. In the second chapter, the behavior of the model solution under general conditions is discussed. The existence of a constant Cdm0 is proved. Such that if the initial value of the unitary weak solution exists as a whole; If the initial free energy functional satisfies F. [U 0] 0 (implies so weak solution at finite time blow-up. in addition. In chapter 3, the global existence of the solution and the finite time blow-up are discussed by limiting the index range. In this index range, the global existence of domain decomposition and the optimal criticality of blow-up at finite time are established. The proof of the optimal criticality depends on the relationship between the free energy functional and the HLS inequality. Chapter 4th discusses the uniqueness of weak solutions. One sex. By using the optimal transmission method, the stability and uniqueness of the global weak entropy solution in the sense of Wasserstein distance are obtained. Chapter 5th gives a summary of the main results of this paper and the prospects for future work.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O175

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