The partial boundary value conditions of nonlinear degenerate parabolic equation

The stability of the solutions to a parabolic equation partial derivative u/partial derivative t = Delta A(u) + Sigma(N)(i=1) b(i)(x, t)D(i)u - c(x, t)u - f (x, t) with homogeneous boundary condition is considered. Since the set {s : A' (s) = a(s) = 0} may have an interior point, the equation is with strong degeneracy and the Dirichlet boundary value condition is overdetermined generally. How to find a partial boundary value condition to match up with the equation is studied in this paper. By choosing a suitable test function, the stability of entropy solutions is obtained by Kruzkov bi-variables method.