Boundary blow-up solutions for logistic-type porous media equations with nonregular source

Abstract

In this paper, we establish the existence, uniqueness and blow-up rate near the boundary of boundary blow-up solutions to the porous media equations of logistic type -Δ u = a(x)u1/m - b(x)f(u) with m > 1. We first consider the existence of such solutions for the general function f(u), and then study the uniqueness and the blow-up rate for the function f(u) whose variation at infinity is not regular. We also note the difference in the treatment of the blow-up rate for the cases where f varies regularly or not regularly at infinity. © 2009 London Mathematical Society.