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

Abstract

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

CLC Number:

O175.29

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

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