Abstract: 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 investigated. The main results are: 1) there exists only one global weak solution which continuously depends on initial value; 2) when t<T₀,the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.

Key words: fast-diffusion, quasilinear, nonlinear boundary conditions, second initial-boundary value problem