Geodesic
On an equilibrium problem for a~two-layer elastic body with a~crack
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 2, pp. 144-153

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We analyze a free boundary value problem describing an equilibrium state of a two-layer elastic body with a crack. The existence of a solution is proved. Invariant integrals over curves surrounding the crack tip are found. Passages to the limit as the rigidity parameter of the layer vanishes are studied.
Keywords: crack, nonlinear boundary conditions, two-layer body, derivative of the energy functional, invariant integrals. 
@article{SJIM_2013_16_2_a12,
     author = {A. M. Khludnev},
     title = {On an equilibrium problem for a~two-layer elastic body with a~crack},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {144--153},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_2_a12/}
}
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A. M. Khludnev. On an equilibrium problem for a~two-layer elastic body with a~crack. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 2, pp. 144-153. http://geodesic.mathdoc.fr/item/SJIM_2013_16_2_a12/