论文标题
一种用于向后热传导问题的微弱技术的变化技术
A variational technique of mollification applied to backward heat conduction problems
论文作者
论文摘要
本文解决了无界域中分数拉普拉斯和时间依赖系数的向后热传导问题。问题模型概括了扩散过程，并且众所周知被严重不良。我们研究了一种基于微弱化的简单而强大的变分正规化技术。在经典的Sobolev平滑度条件下，我们在数据和操作员都嘈杂的实际情况下，在精确解决方案和正则近似之间得出了订单 - 最佳的收敛速率。此外，我们提出了基于Morozov原理的订单最佳的A-posteriori参数选择规则。最后，我们通过包括图像脱张的一些数值示例来说明正则化技术的鲁棒性和效率。
This paper addresses a backward heat conduction problem with fractional Laplacian and time-dependent coefficient in an unbounded domain. The problem models generalized diffusion processes and is well-known to be severely ill-posed. We investigate a simple and powerful variational regularization technique based on mollification. Under classical Sobolev smoothness conditions, we derive order-optimal convergence rates between the exact solution and regularized approximation in the practical case where both the data and the operator are noisy. Moreover, we propose an order-optimal a-posteriori parameter choice rule based on the Morozov principle. Finally, we illustrate the robustness and efficiency of the regularization technique by some numerical examples including image deblurring.
