Determining surface heat flux for noncharacteristic Cauchy problem for Laplace equation

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=0x=0 and the heat flux is sought in the interval 0