Self-similar asymptotics in plain-strain hydraulic fracture propagation problem

In this article the self-consistent plain-strain hydraulic fracture propagation problem is analyzed analytically and numerically. The fracture is loaded by the far-field confining stress and is driven by time dependent fluid flow at the inlet. The similarity method is used to obtain different classes of the self-similar solutions. The algorithm is realized to analyze the evolution of the considered problem to the asymptotic solutions. Well known Spence & Sharp solution proofed to be an asymptotic solution for problem with initial conditions in non zero far-field confining stress case. Khristianovich & Zheltov solution proofed to be a limit self-similar solution for considered problem.