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 were investigated. The main results are: 1) there exists only one global weak solution which continuously depends on initial value; 2) when t0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.