Influence of the heat source location on the stability of the solution to the Cauchy problem

Abstract

In this paper the solution to the Cauchy-type inverse problem for the Laplace’s equation is presented. A modified Tikhonov regularization was applied here. The regularization parameter was chosen using the Morozov principle. The relation between the location of the heat source (function singularity) and the stability of the solution to the inverse problem was analyzed. Variable thermal loads in the area were simulated by changing the location of heat sources along two boundaries of the rectangle calculation domain.