【摘要】 该文研究一类时间Caputo分数阶逆扩散问题.文中应用Landweber迭代法解这一不适定问题分别给出了先验条件和后验条件下迭代次数(正则化参数)的选取准则,并且给出了该方法收敛性的严格数学证明.最后数值实验表明了Landweber迭代方法解该问题的有效性.更多还原

【Abstract】 In this paper,an inverse diffusion problem with the Caputo fractional derivative in time is considered.We prove that such a problem is ill-posed and apply the Landweber iteration method.The selection criteria for the number of iterations(regularization parameter) under both prior and posterior conditions are provided respectively,along with a rigorous mathematical proof of the convergence of the method.Finally,a numerical example is given to illustrate the effectiveness of this method.更多还原