  The paper presents a method for solving hydraulic fracture problems
accounting for the lag. The method consists in matching the outer (basic)
solution neglecting the lag, with the inner (auxiliary) solution of the derived
1D integral equation with conditions, accounting for the lag and asymptotic
behavior of the opening and the net-pressure. The method refers to practically
important cases, when the influence of the local perturbation, caused by the
lag, becomes insignificant at a distance, where the leading plane-state
asymptotics near the fracture front is still applicable. The universal
asymptotics are used for finding the matching constants of the basic (outer)
solution and for formulation of matching condition for the solution of inner
(auxiliary) problem. The method is illustrated by the solution of the Spence
and Sharp plane-strain problem for a fracture propagating symmetrically from
the inlet, where a Newtonian fluid is pumped at a constant rate. It is stated
that the method developed for deep fractures may also serve in the intermediate
range between deep and shallow fractures.
