联系于Laguerre算子的抛物方程求解和加权混合模估计

论文摘要

本文研究偏微分方程?tu=-Lαu+f及其相关的Cauchy问题求解,其中Lα表示Laguerre算子Lα=1/2（-d2/dx2+x2+1/x2（α2-1/4））,α≥-1/2,我们把?t+Lα作为一个抛物型算子s并用抛物型热半群{e-τ（?t+Lα）｝τ＞0来表达演化方程的解.在此基础上,利用Laguerre算子Lα和Hermite算子之间的联系,得到演化方程的经典解及其偏导的点点表达式.另外,我们还讨论了联系于?t+Lα的分数阶空间时间（space-time）非局部方程（?t+Lα）su=-f,0<s<1,对应的延拓问题,并得出了其解的加权混合模估计.

论文目录

文章来源

类型: 硕士论文

作者: 范会莹

导师: 马涛

关键词: 抛物型演化方程,抛物型算子半群,算子,加权混合模估计

来源: 武汉大学

年度: 2019

分类: 基础科学

专业: 数学

单位: 武汉大学

分类号: O175.2

总页数: 34

文件大小: 448K

下载量: 4

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标签：抛物型演化方程论文;  抛物型算子半群论文;  算子论文;  加权混合模估计论文;