The second initial-boundary value problem for a quasilinear parabolic equations with nonlinear boundary conditions

With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigat ed. The main results are : 1) there exists only one global weak solution wh ich continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.