标题： 带有后验内部测量的时空分数阶扩散方程的反源问题 显示英文标题

标题： Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations

摘要： 本文研究了从后验内部测量中求解空间-时间分数阶扩散方程的反源问题。 通过分数阶导数的记忆效应和唯一延拓性质建立了唯一性结果。 对于数值重构，反问题被重新表述为带有Tikhonov正则化的优化问题。 我们使用Levenberg-Marquardt方法从噪声测量中识别未知源。 最后，我们给出一些数值例子来说明所提出算法的效率和准确性。 显示英文摘要

摘要： This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we give some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm.