Asymptotic Analysis to a Parabolic Equation with a Weighted Localized Source

This paper deals with a nonlinear parabolic equation with a complicated source term, which is a product of localized source e^qu(0,t), local source e^{pu(x, t)}, and weight function a(x). We investigate how the three factors influence the asymptotic behavior of solutions. We show that the blow-up set consists of single point {x = 0} if p >; 0; when p ≤ 0 with p + q >; 0, the blow-up takes place everywhere in B. Moreover, the blow-up rate estimation is established with precise coefficients determined.