论文标题
通过sobolev型方程对向后的时间折叠方程的正规化
Regularization of backward time-fractional parabolic equations by Sobolev-type equations
论文作者
论文摘要
考虑到时间分数抛物线方程中嘈杂的最终观察结果的初始条件的问题。这个问题是众所周知的，并且是通过向后sobolev型方程进行正规化的。使用先验和后正规化参数选择规则获得持有人类型的错误估计。提出的正则化方法导致了稳定的非词数方案。理论误差估计通过一维方程的数值测试证实
The problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well-known to be ill-posed and it is regularized by backward Sobolev-type equations. Error estimates of Holder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations
