时空分数阶扩散波动方程的初值识别问题

Identification of Initial Values of Space-Time Fractional Diffusion-Wave Equation

研究具有时空分数阶导数的扩散波动方程的初值识别反问题.分析该反问题的不适定性,给出条件稳定性结果.利用Tikhonov正则化方法恢复解的稳定性,并分别给出在先验和后验正则化参数选取规则下,正则解和精确解之间的误差估计.通过数值算例说明Tikhonov正则化方法求解此类反问题非常有效.

In this paper,we study the identification of unknown initial values of time-space fractional diffusion-wave equation.Firstly,we prove that the problem is ill-posed and give the conditional stability result.Then,we use Tikhonov regularization method to restore the stability of the solutions,and give the convergence error estimates under a priori regularization parameter selection rule and a posteriori regularization parameter selection rule.Finally,numerical examples show that the regularization method is effective.