应用数学2025，Vol.38Issue(3)：636-650,15.
非局部扩散方程内部观测反演源项的唯一性及其数值模拟
Uniqueness of an Inverse Source Problem for Anomalous Diffusion Equation from Interior Domain Observation and Its Numerical Simulation
摘要
Abstract
This article studies the anomalous diffusion equation with multiple fractional time deriva-tives.Firstly,using Laplace transform and the fractional Theta functions,we prove the unique continuation principle of solutions to this equation.Secondly,by combining with the Duhamel principle,we establish the uniqueness result for the inversion of the source term from interior domain observation.In terms of numerical aspects,we convert the inverse problem into an optimization problem and employ a regulariza-tion iterative threshold algorithm for numerical computation.Finally,the accuracy and effectiveness of the algorithm are verified through numerical experiments.关键词
非局部扩散方程/反源问题/唯一延拓性/分数阶Theta函数Key words
Anomalous diffusion equation/Inverse source problem/Unique continuation/Fraction-al Theta function分类
数学引用本文复制引用
陈晨,李志远..非局部扩散方程内部观测反演源项的唯一性及其数值模拟[J].应用数学,2025,38(3):636-650,15.基金项目
国家自然科学基金(12271277) （12271277）
宁波市青年科技创新领军人才(2024QL045) （2024QL045）
