A theorem of the Phragmén-Lindelöf type for solutions of an evolution equation of the second order with respect to time variable

Abstract

We consider a solution u(x, t) of the general linear evolution equation of the second order with respect to time variable given on the ball Π(T) = {(x,t): xε R ⁿ, t ε [0, T]} and study the dependence of the behavior of this solution on the behavior of the functions at infinity.