A note on maximal solutions of nonlinear parabolic equations with absorption

Abstract

If Ω is a bounded domain in R^N and f a continuous nondecreasing function satisfying a super linear growth condition at infinity, we study the existence and uniqueness of solutions for the problem (P): ∂_tu−Δu+f(u)=0 in Q_∞^Ω:=Ω×(0,∞), u=∞ on the parabolic boundary ∂_pQ. We prove that in most cases, the existence and uniqueness is reduced to the same property for the associated stationary equation in Ω.