A note on maximal solutions of nonlinear parabolic equations with absorption

摘要

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 — △u + 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.