Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1705-1718.

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

Xinhai He(),Mei Liu(),Han Yang*()   

  1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756
  • Received:2022-03-15 Online:2022-12-26 Published:2022-12-16
  • Contact: Han Yang;;
  • Supported by:
    the NSFC(11701477);the NSFC(11971394)


The purpose of this paper is to study the Cauchy problem of a class of semilinear time fractional diffusion-wave equations. Based on the Lr-Lq 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