We give sufficient conditions for local solutions to some fourth order semilinear ordinary differential equations to blow up in finite time with wide oscillations, a phenomenon not visible for lower order equations. The result is then applied to several classes of semilinear partial differential equations in order to characterize the blow up solutions including, in particular, its applications to a suspension bridge model. We also give numerical results which describe this oscillating blow up and allow us to suggest several open problems and to formulate some related conjectures.

Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations

GAZZOLA, FILIPPO;PAVANI, RAFFAELLA
2013

Abstract

We give sufficient conditions for local solutions to some fourth order semilinear ordinary differential equations to blow up in finite time with wide oscillations, a phenomenon not visible for lower order equations. The result is then applied to several classes of semilinear partial differential equations in order to characterize the blow up solutions including, in particular, its applications to a suspension bridge model. We also give numerical results which describe this oscillating blow up and allow us to suggest several open problems and to formulate some related conjectures.
nonlinear fourth order differential equation; blow up time; suspension bridges
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/703128
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