Theoretical analysis of the 2D thermal cloaking problem

International Conference on Information Technologies in Business and Industry 2016

计算机科学;经济学;工业技术

Alekseev, G.V.^1 ; Spivak, Yu E.^2 ; Yashchenko, E.N.^3

Institute of Applied Mathematics FEB RAS, Radio Str., 7, Vladivostok

690041, Russia^1

Far Eastern Federal University, D(20), Pen. Ayaks, I. Russky, Vladivostok

690922, Russia^2

Far Eastern Technical Fisheries University, 52B, Lugovaya Str., Vladivostok

690087, Russia^3

关键词: Coefficient inverse problems;    Inhomogeneous anisotropic medium;    Material parameter;    Numerical algorithms;    Optimization method;    Scattering problems;    Stability estimates;    Variable coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/803/1/012001/pdf
DOI  :  10.1088/1742-6596/803/1/012001

来源: IOP

【 摘 要 】

Coefficient inverse problems for the model of heat scattering with variable coefficients arising when developing technologies of design of thermal cloaking devices are considered. By the optimization method, these problems are reduced to respective control problems. The material parameters (radial and azimuthal conductivities) of the inhomogeneous anisotropic medium, filling the thermal cloak, play the role of control. The model of heat scattering acts as a functional restriction. A unique solvability of direct heat scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and efficient numerical algorithm of solving thermal cloaking problems is proposed.