宁夏大学学报（自然科学版）2017，Vol.38Issue(4)：317-321,5.
一类退化抛物型方程反问题的全变差正则化方法
Total Variation Regularization Method for the Inverse Problem of A Degenerate Parabolic Equation
摘要
Abstract
An inverse problem is investigated by using subsidiary condition to reconstruct the radiation coefficient of the second order degenerate parabolic equation.Based on the optimal control framework and total variation regularization,the problem is transformed into an optimization problem.Subsidiary condition in this paper is an average sense of observation,rather than a general terminal observation.Due to the total variation term is non-differential,so it is hard to work out the uniqueness of optimal solution.In order to overcome this difficulty,a polished total variation regularization term is introduced.Furthermore,the existence and the necessary conditions of the optimal solution are discussed.Finally,it is proved that the uniqueness and stability of the minimizer is proved successfully when the terminal time is assumed to be relativelv small.关键词
反问题/退化抛物型方程/全变差正则化/最优控制/存在性/唯一性/稳定性Key words
inverse problem/degenerate parabolic equation/total variation regularization/optimal control/existence/uniqueness/stability分类
数理科学引用本文复制引用
张泰年,曾剑..一类退化抛物型方程反问题的全变差正则化方法[J].宁夏大学学报（自然科学版）,2017,38(4):317-321,5.基金项目
国家自然科学基金资助项目(11261029,11461039) （11261029,11461039）
甘肃省自然科学基金资助项目(145RJZA124) （145RJZA124）
