  The equation arising from Prandtl boundary layer theory is considered. The
existence of the entropy solution can be proved by BV estimate method. The
interesting problem is that, since a may be degenerate on the boundary, the
usual boundary value condition may be overdetermined. Accordingly, only
dependent on a partial boundary value condition, the stability of solutions can
be expected. This expectation is turned to reality by Kruzkov's bi-variables
method, a reasonable partial boundary value condition matching up with the
equation is found first time. Moreover, the stability can be proved even
without any boundary value condition.
