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

Abstract

This paper deals with classical solutions of quasilinear equations of the form $$ [\rho(\mathbf{x},t,u,\nabla u)u,_i],_i = u,_t $$ in a semi--infinite cylinder in $\Bbb R^3$ with homogeneous initial data and with homogeneous Dirichlet data prescribed on the lateral surface for all time. Under appropriate assumptions on the form of $\rho$, Phragmen--Lindelöf type growth--decay estimates are derived.