Geodesic
Asymptotic Analysis of Hydraulic Fracture Crack Process Growth
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 105-116.

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In this work the self-similar solution of a problem of propagation of hydraulic fracture crack is presented. It is proposed that a crack is focused vertically and research of of its development process is analyzed within the coupled problem of the hydrodynamics theory (flow of viscous fluids) and the linear theory of elasticity (fracture crack growth). Asymptotics of the self-similar solution at the long and small distances from tip of a crack were obtained. Simple approximations of the solution in all length range are offered.
Keywords: hydraulic fracture crack, self-similar solution, asymptomatically analysis. 
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V. I. Astaf'ev. Asymptotic Analysis of Hydraulic Fracture Crack Process Growth. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 105-116. http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a11/

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