@ARTICLE{Ciałkowski_Michał_The_2023,
 author={Ciałkowski, Michał and Joachimiak, Magda and Mierzwiczak, Magdalena and Frąckowiak, Andrzej and Olejnik, Aleksander and Kozakiewicz, Adam},
 volume={vol. 44},
 number={No 4},
 journal={Archives of Thermodynamics},
 pages={563-579},
 howpublished={online},
 year={2023},
 publisher={The Committee of Thermodynamics and Combustion of the Polish Academy of Sciences and The Institute of Fluid-Flow Machinery Polish Academy of Sciences},
 abstract={Ceramic protective coats, for instance, on turbine blades, create a double-layer area with various thermophysical properties and they require metal temperature control. In this paper, it is implemented by formulating a Cauchy problem for the equation of thermal conductivity in the metal cylindrical area with a ceramic layer. Due to the ill posed problem, a regularization method was applied consisting in the notation of thermal balance for the ceramic layer. A spectral radius for the equation matrix was taken as the stability measure of the Cauchy problem. Numerical calculations were performed for a varied thickness of the ceramic layer, with consideration of the non-linear thermophysical properties of steel and a ceramic layer (zirconium dioxide). A polynomial was determined which approximates temperature distribution in time for the protective layer. The stability of solutions was compared for undisturbed and disturbed temperature values, and thermophysical parameters with various ceramic layer thickness. The obtained calculation results confirmed the effectiveness of the proposed regularization method in obtaining stable solutions at random data disturbance.},
 type={Article},
 title={The analysis of the stability of the Cauchy problem in the cylindrical double-layer area},
 URL={http://www.czasopisma.pan.pl/Content/131165/PDF/art28_638.pdf},
 doi={10.24425/ather.2023.149735},
 keywords={cauchy problem, quasiregularization method, protective layer, cylindrical double-layer area},
}