Two-dimensional inverse heat conduction problem in a quarter plane: integral approach

摘要

We consider a two-dimensional inverse heat conduction problem in the region {x>0,y>0} with infinite boundary which consists to reconstruct the boundary condition f(y,t)=u(0,y,t) on one side from the measured temperature g(y,t)=u(1,y,t) on accessible interior region. The numerical solution of the direct problem is computed by a boundary integral equation method. The inverse problem is equivalent to an ill-posed integral equation. For its approximation we use the regularization of Tikhonov after the mollification of the noised data g delta of exact data g. We show some numerical examples to illustrate the validity of the method.