Mathematical models of a hydraulic shock

In the present paper, we derive macroscopic mathematical models of the pressure distribution field near the oil well during the hydraulic shock. To get these models we follow the scheme, suggested by J. Keller and R. Burridge. This scheme is based upon a rigorous homogenization of the exact mathematical model, describing on a microscopic level the joint motion of an elastic solid skeleton and a viscous fluid filling the pores.