Determining surface heat flux for noncharacteristic Cauchy problem for Laplace equation

Abstract

In this paper, the noncharacteristic Cauchy problem for the Laplace equation {wxx+wyy=0x∈(0,1),y∈R,w(0,y)=g(y)y∈R,wx(0,y)=h(y)y∈R, is investigated, where the Cauchy data is given at x=0 and the heat flux is sought in the interval 0<x≤1. This problem is severely ill-posed: the solution (if it exists) does not depend continuously on the given data. A modified regularization method is used to solve this problem. Furthermore, some error estimates for the heat flux between the regularization solution and the exact solution are given. Finally, a numerical example shows that the proposed method works well.