Abstract: We studied the asymptotic behavior of solutions for a class of  initial-boundary value problems of a semilinear parabolic equation with boundary degeneracy by using the methods of weighted energy estimates and constructing self-similar upper solutions. We obtained the global existence and blowing-up properties of solutions to the problem,  established Fujita type theorem, and characterized the quantitative relationship between the critical Fujita exponent and the degenerate diffusion term and the nonlinear source term.

Key words:  , boundary degeneracy, critical Fujita exponent, semilinear parabolic equation