The Quasi-reversibility Method to Solve the Cauchy Problems for Parabolic Equations  

作　　者：Jing LI Bo Ling GUO 

机构地区：[1]School of Mathematics and Computational Science,Changsha University of Science and Technology [2]Institute of Applied Physics and Computational Mathematics

出　　处：《Acta Mathematica Sinica,English Series》2013年第8期1617-1628,共12页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11226166);Scientific Research Fund of Hu'nan Provincial Education Department (Grant No.11C0052)

摘　　要：In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain of QT with strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameter ε that we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitude δ tends to zero.

关 键 词：Ⅲ-posed problems parabolic equations Cauchy problems QUASI-REVERSIBILITY 

分 类 号：R575.2[医药卫生—消化系统]