Geodesic
Optimization method in problems of acoustic cloaking of material bodies
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1477-1493

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Optimization problems for a three-dimensional model of acoustic scattering are formulated and studied. These problems arise in designing tools for cloaking material bodies by applying the wave flow method. The cloaking effect is achieved due to an optimal choice of variable parameters of the inhomogeneous isotropic medium occupying the sought shell. The solvability of direct and optimization problems for the acoustic scattering model is proved, and sufficient conditions ensuring the uniqueness and stability of optimal solutions are established. 
@article{ZVMMF_2017_57_9_a5,
     author = {G. V. Alekseev and A. V. Lobanov and Yu. E. Spivak},
     title = {Optimization method in problems of acoustic cloaking of material bodies},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1477--1493},
     publisher = {mathdoc},
     volume = {57},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a5/}
}
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G. V. Alekseev; A. V. Lobanov; Yu. E. Spivak. Optimization method in problems of acoustic cloaking of material bodies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1477-1493. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a5/