  The paper treats the propagation of a hydraulically driven crack. We
explicitly write the local speed equation, which facilitates using the theory
of propagating interfaces. It is shown that when neglecting the lag between the
liquid front and the crack tip, the lubrication PDE yields that a solution
satisfies the speed equation identically. This implies that for zero or small
lag, the boundary value problem appears ill-posed when solved numerically. We
suggest e - regularization, which consists in employing the speed equation
together with a prescribed BC on the front to obtain a new BC formulated at a
small distance behind the front rather than on the front itself. It is shown
that - regularization provides accurate and stable results with reasonable time
expense. It is also shown that the speed equation gives a key to proper choice
of unknown functions when solving a hydraulic fracture problem numerically.
