求解时空分数阶扩散方程反源问题的数值方法
A Numerical Method for Solving the Inverse Source Problem of the Space-Time Fractional Diffusion Equation
摘要:
在本文中，主要研究一类时空分数阶扩散方程只与空间变量有关的反源问题，通过分析该反源问题的不适定性，将求解反源问题转化求解第一类Fredlom积分方程，应用经典的Tikhonov正则化方法得到了正则解的存在性，并证明正则解在后验正则化参数选择规则下的收敛估计。
Abstract:
In this paper, we mainly study the inverse source problem of a class of space-time fractional diffusion equations which are only related to spatial variables. By analyzing the ill-posedness of the inverse source problem, we transform the solution of the inverse source problem into the solution of the first Fredlom integral equation. The existence of the regular solution is obtained by using the classical Tikhonov regularization method, and the convergence estimation of the regular solution is proved under the posterior regularization parameter selection rule.
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