一类半线性时间分数阶扩散-波动方程解的整体存在唯一性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1705-1718.

一类半线性时间分数阶扩散-波动方程解的整体存在唯一性

何鑫海(),刘梅(),杨晗*()

^{西南交通大学数学学院, 成都 611756}

收稿日期:2022-03-15 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 杨晗 E-mail:xinhaihe@my.swjtu.edu.cn;meiliu@my.swjtu.edu.cn;hanyang95@263.net
作者简介:何鑫海, E-mail: xinhaihe@my.swjtu.edu.cn|刘梅, E-mail: meiliu@my.swjtu.edu.cn
基金资助:
国家自然科学基金(11701477);国家自然科学基金(11971394)

Existence and Uniqueness of Global Solutions for a Class of Semilinear Time Fractional Diffusion-Wave Equations

Xinhai He(),Mei Liu(),Han Yang*()

^{School of Mathematics, Southwest Jiaotong University, Chengdu 611756}

Received:2022-03-15 Online:2022-12-26 Published:2022-12-16
Contact: Han Yang E-mail:xinhaihe@my.swjtu.edu.cn;meiliu@my.swjtu.edu.cn;hanyang95@263.net
Supported by:
the NSFC(11701477);the NSFC(11971394)

摘要/Abstract

摘要：

该文研究一类半线性时间分数阶扩散-波动方程的柯西问题, 基于线性问题的L_r-L_q估计, 通过整体迭代法, 在小初值的情况下研究非线性项指数对于解的整体存在性影响, 在指数满足一定条件的情况下证明了整体解的存在唯一性.

关键词: 时间分数阶扩散-波动方程, 柯西问题, 小初值, 整体解

Abstract:

The purpose of this paper is to study the Cauchy problem of a class of semilinear time fractional diffusion-wave equations. Based on the L^r-L^q estimates obtained from the corresponding linear problem, and combined with the global iteration method, the influence of the exponential of the nonlinear term on the global existence of the solutions is studied with small data, the existence and uniqueness of global solutions are proved under certain conditions of exponential.

Key words: Time fractional diffusion-wave equation, Cauchy problem, Small data, Global solution

中图分类号:

O175.29

何鑫海,刘梅,杨晗. 一类半线性时间分数阶扩散-波动方程解的整体存在唯一性[J]. 数学物理学报, 2022, 42(6): 1705-1718.

Xinhai He,Mei Liu,Han Yang. Existence and Uniqueness of Global Solutions for a Class of Semilinear Time Fractional Diffusion-Wave Equations[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1705-1718.

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