Geodesic
Optimal shapes of cracks in a viscoelastic body
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 294-304

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We consider an optimal control problem for equations describing the quasistatic deformation of a linear viscoelastic body. There is a crack in the body, and displacements of opposite faces of the crack are constrained by the nonpenetration condition. The continuous dependence of the solution to the equilibrium problem on the shape of the crack is established. In particular, we prove the existence of a shape for which the crack opening is minimal
Keywords: viscoelasticity; crack; nonpenetration condition; optimal control; fictitious domain method. 
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     author = {V. V. Shcherbakov and O. I. Krivorot'ko},
     title = {Optimal shapes of cracks in a viscoelastic body},
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     publisher = {mathdoc},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a28/}
}
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V. V. Shcherbakov; O. I. Krivorot'ko. Optimal shapes of cracks in a viscoelastic body. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 294-304. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a28/