Phragmén–Lindelöf alternative of exponential type for the solutions of a fourth order dispersive equation

Abstract

In a recent paper (R. Quintanilla, G. Saccomandi. Quarterly Applied Mathematics, 44, (2006) 547–560) we investigated the spatial behavior of a linear equation of fourth order which models several mechanical situations where dispersive e¤ects are taken into account. We proved a polynomial decay estimate for the solutions of this equation. In the present note we improve this result and we show a Phragmén–Lindelöf alternative of exponential type.