非线性Fokker-Planck型方程在Maxwellian附近解的全局存在性和衰减速率

论文摘要

本文旨在研究非线性Fokker-Planck方程和非线性Vlasov-Poisson-Fokker-Planck方程的解。研究内容包括以下两个方面:一、研究全空间中非线性Fokker-Planck方程在Maxweillian附近解的全局存在性和衰减速率。通过一致能量估计和由Picard迭代构造的局部解来得到解的全局存在性。利用线性Fokker-Planck算子精确的谱分析和能量方法得到非线性模型的衰减速率。其中,模型的非线性给能量估计带来了新的困难,这可以通过对υ加权并且适合Fokker-Planck算子的能量估计来解决。二、建立全空间中非线性Vlasov-Poisson-Fokker-Planck方程光滑解到全局Maxwellian的指数衰减,模型宏观部分和Fokker-Planck算子的非线性耦合给能量估计带来了困难,这可以用类似一中的方法解决。

论文目录

文章来源

类型: 硕士论文

作者: 王倩蓉

导师: 廖杰

关键词: 非线性方程,全局存在性,衰减速率,一致能量估计

来源: 华东理工大学

年度: 2019

分类: 基础科学

专业: 数学

单位: 华东理工大学

分类号: O175

DOI: 10.27148/d.cnki.ghagu.2019.000159

总页数: 46

文件大小: 1598k

下载量: 2

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标签：非线性方程论文;  全局存在性论文;  衰减速率论文;  一致能量估计论文;