Blow-up profile for solutions of a fourth order nonlinear equation

Authors: D'Ambrosio, Lorenzo; Lessard, Jean-Philippe; Pugliese, Alessandro
Abstract: It is well known that the nontrivial solutions of the equation u¿(r)+¿u¿(r)+f(u(r))=0u¿(r)+¿u¿(r)+f(u(r))=0 blow up in finite time under suitable hypotheses on the initial data, ¿¿ and ff. These solutions blow up with large oscillations. Knowledge of the blow-up profile of these solutions is of great importance, for instance, in studying the dynamics of suspension bridges. The equation is also commonly referred to as extended Fisher–Kolmogorov equation or Swift–Hohenberg equation. In this paper we provide details of the blow-up profile. The key idea is to relate this blow-up profile to the existence of periodic solutions for an auxiliary equation.
Document Type: Article de recherche
Issue Date: 1 July 2015
Open Access Date: 1 July 2017
Document version: AM
Permalink: http://hdl.handle.net/20.500.11794/1341
This document was published in: Nonlinear analysis, Vol. 121, 280–335 (2015)
https://doi.org/10.1016/j.na.2014.12.026
Elsevier
Alternative version: 10.1016/j.na.2014.12.026
Collection:Articles publiés dans des revues avec comité de lecture

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