Counter streams of solutions of degenerating parabolic equations

The mathematical model is process for a process of the formation of counter streams of some physical quantity, for instance, temperature, concentration of a substance, velocity of a fluid. The nonlinear degenerate parabolic equations describing this process change the direction of evolution depending on the sign of their solutions. For such equations the problem of the counter streams is studied. At the initial and final moments the values of the solution, agreed with the direction of evoluation of the equation, are prescribed.
The method of an elliptic regularization is applied. This technique works good in the numerical calculations of the similar problems. Obtained estimates are uniform in the parameter of the regularizations and make possible to realize the passage to the limit on this parameter.