On the finite space blow up of the solutions of the Swift-Hohenberg equation

Abstract: The aim of this paper is to study the finite space blow up of the solutions for a class of fourth order differential equations. Our results answer a conjecture in [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations. Arch. Ration. Mech. Anal., 207(2):717--752, 2013] and they have implications on the nonexistence of beam oscillation given by traveling wave profile at low speed propagation.