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

Abstract

We consider a two-dimensional inverse heat conduction problem in the region $$\lbrace x>0, y >0 \rbrace $$ 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.