Fujita type theorems for a class of semilinear parabolic equations with a gradient term

This paper concerns the asymptotic behavior of solutions to the Neumann exterior problem of a class of semilinear parabolic equations with a gradient term. The blowup theorem of Fujita type is established and the critical Fujita exponent is formulated by spacial dimension, the behavior of the coefficient of the gradient term at infinity and other exponents.