The Backward Heat Conduction Problem With Variable Coefficients in a Spherical Domain
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摘要: 考虑了一类球型区域上变系数反向热传导问题.这个问题是不适定的，即问题的解（若存在）并不连续依赖于测量数据.构造了投影迭代正则化方法，得到了该反问题的正则近似解，同时给出了在先验和后验参数选取规则下精确解与正则近似解之间的收敛性误差估计.最后，通过数值结果验证了该方法的有效性.Abstract: The backward heat conduction problem with variable coefficients in a spherical domain was considered. This problem is ill-posed, i.e., the solution (if it exists) to this problem does not depend continuously on the measured data. A projected iteration regularization method was constructed to obtain the regularized approximate solution to this inverse problem, and the convergence error estimates between the exact solution and the corresponding regularized approximate solution were given under the a priori and a posteriori parameter choice rules. Numerical results verify the effectiveness of this method.
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