A New Regularization Method for a Parameter Identification Problem in a Non-linear Partial Differential Equation  

作　　者：NAIR M.Thamban ROY Samprita Das 

机构地区：[1]Department of Mathematics,BITS Pilani,K K Birla Goa Campus,Zuarinager,Goa 403726,India [2]Department of Mathematics and Statistics,IISER Kokota,Nadia,West Bengal 741246,India

出　　处：《Journal of Partial Differential Equations》2023年第2期147-190,共44页偏微分方程（英文版）

摘　　要：We consider a parameter identification problem associated with a quasilinear elliptic Neumann boundary value problem involving a parameter function a(-)and the solution u(-),where the problem is to identify a(-)on an interval I:=g(F)from the knowledge of the solution u()as g on I,where F is a given curve on the boundary of the domain CR^(3) of the problem and g is a continuous function.The inverse problem is formulated as a problem of solving an operator equation involving a compact operator depending on the data,and for obtaining stable approximate solutions under noisy data,a new regularization method is considered.The derived error estimates are similar to,and in certain cases better than,the classical Tikhonov regularization considered in the literature in recent past.

关 键 词：ILL-POSED REGULARIZATION parameter identification 

分 类 号：O175.29[理学—数学]