A Phragmén-Lindelöf alternative for a class of quasilinear second order parabolic problems

This paper deals with classical solutions of quasilinear equations of the form [ρ(x,t,u,∇ u)u,ᵢ],ᵢ = u,ₜ in a semi--infinite cylinder in R³ with homogeneous initial data and with homogeneous Dirichlet data prescribed on the lateral surface for all time. Under appropriate assumptions on the form of ρ, Phragmen--Lindelöf type growth--decay estimates are derived.