Refined blow-up results for nonlinear fourth order differential equations

Filippo Gazzola; Paschalis Karageorgis

doi:10.3934/cpaa.2015.14.677

Article Contents

2015, Volume 14, Issue 2: 677-693. Doi: 10.3934/cpaa.2015.14.677

This issue Previous Article Hopf bifurcation in an age-structured population model with two delays Next Article Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system with cubic nonlinearities in $\mathbb{R}^2$

Refined blow-up results for nonlinear fourth order differential equations

Filippo Gazzola^1, and
Paschalis Karageorgis^2,

1.
Dipartimento di Matematica Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano
2.
School of Mathematics, Trinity College, Dublin 2

Received: April 30, 2014

Revised: September 30, 2014

Published: February 2015

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Abstract

We study a class of nonlinear fourth order differential equations which arise as models of suspension bridges. When it comes to power-like nonlinearities, it is known that solutions may blow up in finite time, if the initial data satisfy some positivity assumption. We extend this result to more general nonlinearities allowing exponential growth and to a wider class of initial data. We also give some hints on how to prevent blow-up.

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Mathematics Subject Classification: 34A12, 65L05, 34C10, 35B05.

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