Self-similar solution of hydraulic fracture problem for poroelastic medium

In the paper we present solution of coupled hydraulic fracture problem in view of deformation of poroelastic medium and porous media flow. The formation of crack and its growth are influenced by Newtonian fluid pumped through well. Solution self-similar sets are constructed. These solutions are used to describe the evolution of a penny shaped crack in poroelastic medium with a uniform pressure inside within the fracture. The present paper is part of a series of publications on hydraulic fracturing, which are based on the splitting of the original equations to components in accordance with an incomplete coupling principle.