论文标题
及时求解热方程的平均值方法
Mean value methods for solving the heat equation backwards in time
论文作者
论文摘要
我们研究了一种迭代（和高度不足）的迭代平均值方法，即及时求解热方程。半组理论用于重写逆问题的解决方案作为仿期算子的固定点方程的解，线性部分满足特殊功能分析属性。我们给出了该方法的收敛证明，并获得残差的收敛速率。在所谓的源条件下也获得了迭代率的收敛速率。
We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed point equation for an affine operator, with linear part satisfying special functional analytical properties. We give a convergence proof for the method and obtain convergence rates for the residual. Convergence rates for the iterates are also obtained under the so called source conditions.
