The diffusion of a discontinuity of the shear stress at the boundary of a viscoplastic half-plane

For the problem of the diffusion of a discontinuity of the shear stress at the boundary of a half-plane, which is a special case of the general problem of the diffusion of a vortex layer, the classes of media and types of assignment of boundary conditions for which self-similar solutions exist are discussed. For a viscoplastic medium in a half-plane the problem reduces to the problem in a layer of time-variable thickness, the solution of which does not possess the property of analyticity. The long-term asymptotic of this problem are investigated. In the case where, at an accessible boundary, it is possible simultaneously to measure both the shear stress and the horizontal velocity, an algorithm is proposed for finding a quantity that is difficult to measure, A namely, the thickness of the zone of viscoplastic flow.