某些数学物理反问题的研究及其算法设计分析

We studied some inverse and ill-posed problems for partial differential equations which arise from engineering and sciences. These inverse and ill-posed problems are very important for both.applied mathematics research and researches in other fields and they are very difficult. We discussed the uniqueness and stability for the inverse and ill-posed problem theoretically. For numerical computation, we showed how to construct the stable algorithms and.realize them in the computers. Some error estimations and convergence rates were obtained. For these problems, we proposed some method which have been shown effective. It is hopeful that these methods can be used to solve the inverse and ill-posed problems in other fields.

该项目研究某些数学物理反问题,其中包括物理中裂纹的位置确定问题,被腐蚀边界的确定问题等.此类问题可归纳为偏微分方程的系数或边界的确定问题.这类问题往往是不适应和非线性的.我们讨论在怎样的条件下,该问题具有唯一性和条件稳定性,在此基础上,我们将提出稳定的正则化算法,并进行算法设计分析.该项成果将为许多实际问题提供方法.