Geodesic
Solution of periodic boundary-value problems of the spatial theory of elasticity in the vector form
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 59-69.

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We discuss boundary-value problems for the system of equations of the spatial theory of elasticity in the class of double-periodic functions and obtain a general solution of the system. We distinguish six types of elementary Floquet waves and examine their energy characteristics. We consider fundamental boundary-value problems in the half-space in the vector form. The diffraction problem for an elastic wave on a periodic system of defects in the vector form is reduced to the paired summator functional equation.
Keywords: periodic system, theory of elasticity, Floquet wave. 
@article{INTO_2017_139_a5,
     author = {E. A. Osipov},
     title = {Solution of periodic boundary-value problems of the spatial theory of elasticity in the vector form},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {59--69},
     publisher = {mathdoc},
     volume = {139},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_139_a5/}
}
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E. A. Osipov. Solution of periodic boundary-value problems of the spatial theory of elasticity in the vector form. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 59-69. http://geodesic.mathdoc.fr/item/INTO_2017_139_a5/