带有时间独立反应系数的抛物方程逆时问题的稳定性（英文）

Stability of the backward problem of parabolic equation with time-dependent reaction coefficient

考虑了带有时间独立系数的二维抛物方程的逆时问题.此问题具有严重的不适定性,即解(若存在)不连续依赖于给定的数据.利用正则化方法,得到了解的最优稳定估计.数值算例展示了该正则化方法的有效性.

The backward problem of two-dimensional parabolic equation with a time-dependent coefficient was considered.This problem is severely ill-posed,i.e.,the solution(if it exists)does not depend continuously on the given data.Using the method of regularization,an optimal stability estimation of the solution was derived.A numerical example shows the effectiveness of the presented method.