A method of solving the diffusion problem for a vortex layer in a viscoplastic half-plane

A method is proposed to reduce the classical formulation of the problem to a system of two functional equations whose solution can be found numerically. A number of assertions that characterize the behavior of a rigid zone are proved. In particular, the lower estimate h ⁰(t) = 2b√t for the boundary motion is obtained; an explicit expression for b is given as a boundary stress function.