On the evolutionary p-Laplacian equation with a partial boundary value condition

Consider the equation u(t) = div(d(alpha)|del u|(p-2)del u) + partial derivative b(i)(u, x, t)/partial derivative x(i), (x,t) is an element of Omega x (0, T), where Omega is a bounded domain, d(x) is the distance function from the boundary partial derivative Omega. Since the nonlinearity, the boundary value condition cannot be portrayed by the Fichera function. If alpha < p - 1, a partial boundary value condition is portrayed by a new way, the stability of the weak solutions is proved by this partial boundary value condition. If alpha > p - 1, the stability of the weak solutions may be proved independent of the boundary value condition.