时间反向热传导问题的拟逆正则化方法及误差估计

The Quasi-Reversibility Regularization Method and Error Estimate for the Time-Inverse Heat Conduction Problem

该文讨论了时间反向热传导问题,该问题是严重不适定问题,它的解在一定条件下存在但不连续依赖于数据,这给数据处理带来了很大的不便.该文给出一个简单便捷的拟逆正则化方法来恢复解对数据的连续依赖性.根据拟逆正则化问题构造正则解,在先验正则化参数选取规则下,给出了该问题的近似解和精确解之间的误差估计,并用数值算例表明该方法是有效的.

The backward heat conduction problem in time is considered,although its solution exists but discontinuously depends on the data.It is very inconvenient for numerical computation,so a simple and convenient new quasi-reversibility regularization method is proposed to restore the continuous dependence of the solution on the data.The regularization solution is obtained according to the quasi-reversibility regularization problem.Meanwhile,the convergence of errors between the approximate solution and the exact solution for the ill-posed problem is estimated,and the priori regularization parameter selection rules of the method are given.A numerical example is made to demonstrate the effectiveness of the proposed method.