Asymptotic Analysis to a Parabolic Equation with a Weighted Localized Source
Linghua Kong, Xueda Zhao, Bo Liang · 2012
This paper deals with a nonlinear parabolic equation with a complicated source term, which is a product of localized source equ(0,t), local source epu(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.