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Wide Oscillation Finite Time Blow Up for Solutions to Nonlinear Fourth Order Differential Equations

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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 of 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.

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Authors and Affiliations

  1. Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, 20133, Milan, Italy

    Filippo Gazzola & Raffaella Pavani

Authors
  1. Filippo Gazzola
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  2. Raffaella Pavani
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Correspondence to Filippo Gazzola.

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Communicated by P. Rabinowitz

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Gazzola, F., Pavani, R. Wide Oscillation Finite Time Blow Up for Solutions to Nonlinear Fourth Order Differential Equations. Arch Rational Mech Anal 207, 717–752 (2013). https://doi.org/10.1007/s00205-012-0569-5

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  • DOI: https://doi.org/10.1007/s00205-012-0569-5

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