Refined blow-up results for nonlinear fourth order differential equations | Zendy

Filippo Gazzola | Zendy; Paschalis Karageorgis | Zendy

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Refined blow-up results for nonlinear fourth order differential equations

Author(s) -

Filippo Gazzola,

Paschalis Karageorgis

Publication year - 2015

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2015.14.677

Subject(s) - nonlinear system , class (philosophy) , mathematics , order (exchange) , differential equation , suspension (topology) , exponential function , mathematical analysis , exponential growth , first order , differential (mechanical device) , computer science , physics , pure mathematics , homotopy , thermodynamics , artificial intelligence , finance , quantum mechanics , economics

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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