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

被引：9
|
作者：
D'Ambrosio, Lorenzo [1 ]
Lessard, Jean-Philippe [2 ]
Pugliese, Alessandro [1 ]
机构：
[1] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy
[2] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6, Canada
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 121卷
关键词：
Suspension bridges; Fisher-Kolmogorov; Swift-Hohenberg; Blow-up profile; Computer assisted proof;
D O I：
10.1016/j.na.2014.12.026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that the nontrivial solutions of the equation u ''''(r) + kappa u ''(r) + f (u(r)) = 0 blow up in finite time under suitable hypotheses on the initial data,. and f. 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. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：280 / 335
页数：56
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