多项时间分数阶抛物型方程反源问题的拟逆方法  

A Quasi-Inverse Method for Inverse Problems of Parabolic Equationsof the Time Fractional Order

作　　者：王雨欣 

机构地区：[1]西北师范大学数学与统计学院, 甘肃 兰州

出　　处：《应用数学进展》2023年第6期2861-2875,共15页Advances in Applied Mathematics

摘　　要：本文利用分数阶拟逆方法解决多项时间分数阶抛物型方程的反源问题,该反问题是不适定的。 首先给出了反问题的条件稳定性,然后提出分数阶拟逆方法,即在原方程中引入了与椭圆微分算子 有关的新的扰动项,最后基于多项Mittag-Leffler函数的一些性质,在理论上我们给出了正则化解在先验正则化参数选择规则下相应的收敛速度。In this paper, the fractional quasi-inverse method is used to solve the inverse source problem of polynomial time fractional parabolic equations, which is ill-posed. First- ly, the conditional stability of the inverse problem is given, and then the fractional quasi-inverse method is proposed, that is, the perturbation term related to elliptic differential operator is introduced into the original equation. Finally, based on some properties of Mittag-Leffler function, the corresponding convergence rate of the regu- lar solution under the prior selection rule is given in theory.

关 键 词：多项时间分数阶抛物型方程的反源问题 拟逆正则化方法 误差估计 

分 类 号：G63[文化科学—教育学]