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

页码：280 / 335

页数：56

共 50 条

[31] Uniform blow-up profile and boundary behaviour for a non-local reaction-diffusion equation with critical damping [J].

Souplet, P .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2004, 27 (15) :1819-1829

[32] Many-body blow-up profile of boson stars with external potentials [J].

Dinh-Thi Nguyen .

REVIEWS IN MATHEMATICAL PHYSICS, 2019, 31 (10)

[33] Rigorous numerical inclusion of the blow-up time for the Fujita-type equation [J].

Mizuguchi, Makoto ;

Sekine, Kouta ;

Hashimoto, Kouji ;

Nakao, Mitsuhiro T. ;

Oishi, Shin'ichi .

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2023, 40 (01) :665-689

[34] Rigorous numerical inclusion of the blow-up time for the Fujita-type equation [J].

Makoto Mizuguchi ;

Kouta Sekine ;

Kouji Hashimoto ;

Mitsuhiro T. Nakao ;

Shin’ichi Oishi .

Japan Journal of Industrial and Applied Mathematics, 2023, 40 :665-689

[35] Type II blow-up mechanisms in a semilinear heat equation with Lepin exponent [J].

Seki, Yukihiro .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (03) :853-900

[36] Blow-up rate and profile for a degenerate parabolic system coupled via nonlocal sources [J].

Zheng, Sining ;

Wang, Lidong .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 52 (10-11) :1387-1402

[37] Existence of homoclinic solutions for a fourth order differential equation with a parameter [J].

Li, Tiexiang ;

Sun, Juntao ;

Wu, Tsung-Fang .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 251 :499-506

[38] BLOW-UP RESULTS FOR A STRONGLY PERTURBED SEMILINEAR HEAT EQUATION: THEORETICAL ANALYSIS AND NUMERICAL METHOD [J].

Van Tien Nguyen ;

Zaag, Hatem .

ANALYSIS & PDE, 2016, 9 (01) :229-257

[39] Refined Regularity of the Blow-Up Set Linked to Refined Asymptotic Behavior for the Semilinear Heat Equation [J].

Ghoul, Tej-Eddine ;

Van Tien Nguyen ;

Zaag, Hatem .

ADVANCED NONLINEAR STUDIES, 2017, 17 (01) :31-54

[40] A blow-up result for the travelling waves of the pseudo-relativistic Hartree equation with small velocity [J].

Wang, Qingxuan .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (13) :10403-10415

← 1 2 3 4 5 →