The parabolic logistic equation with blow-up initial and boundary values

Abstract

In this article, we investigate the parabolic logistic equation with blow-up initial and boundary values... We study the existence and uniqueness of positive solutions, and their asymptotic behavior near the parabolic boundary. Under the extra condition that b(x, t) ≥ c(T - t)⁰d(x,∂Ω)ᵝ on Ω x [0,T) for some constants c > 0,Ɵ > and β > -2, we show that such a solution stays bounded in any compact subset of Ω as t increases to T, and hence solves the equation up to t = T.