论文标题
通过多项式回归和共轭梯度法估计时间依赖源项和初始温度的逆问题
An inverse problem in estimating the time dependent source term and initial temperature simultaneously by the polynomial regression and conjugate gradient method
论文作者
论文摘要
从最终和内部温度测量值中，同时使用初始温度识别源项的是一个反热传导问题，这是一种不适的。最佳控制框架已被发现有效解决这些问题。但是，他们需要找到梯度信息。这项研究已采用了这个想法。我们得出了Tikhonov功能的梯度，并从必要条件中建立了最小化器的稳定性。为各种测试示例提供了进化算法的稳定性和有效性。
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be effective in dealing with these problems. However, they require to find the gradient information. This idea has been employed in this research. We derive the gradient of Tikhonov functional and establish the stability of the minimizer from the necessary condition. The stability and effectiveness of the evolutionary algorithm are presented for various test examples.
