一类半线性分数阶σ-发展方程解的整体存在唯一性  

Global Existence and Uniqueness for Semi-linear Fractional σ-Evolution Equations

作　　者：陈雪丽 何鑫海 杨晗[1] CHEN Xueli;HE Xinhai;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《应用数学》2023年第3期674-683,共10页Mathematica Applicata

基　　金：国家自然科学基金(11701477,11971394)。

摘　　要：本文研究一类半线性时间分数阶σ-发展方程的Cauchy问题.利用改进的Bessel函数得到相应线性齐次问题解的能量估计,通过整体迭代法,在小初值情形下证明了在非线性项指数满足一定条件的情况下解的整体存在唯一性.本文在特殊情形下所得结论的极限与经典结论一致.The purpose of this paper is to study the Cauchy problem of a class of semi-linear time fractional σ-evolution equations.By using modified Bessel functions,the energy estimates for solutions to the corresponding linear homogeneous equations are obtained,the global existence and uniqueness of solutions is then proved by global iteration method in the case of small data when the nonlinear exponential satisfies certain conditions.The limit of the conclusion obtained in this paper is consistent with the classical conclusion in special cases.

关 键 词：时间分数阶σ-发展方程 CAUCHY问题 整体迭代法 整体解 

分 类 号：O175.29[理学—数学]