Blow-up of solutions for a nonlinear beam equation with fractional feedback

Soraya Labidi; Nasser Eddine Tatar

doi:10.1016/j.na.2010.10.012

Blow-up of solutions for a nonlinear beam equation with fractional feedback

Soraya Labidi
, Nasser Eddine Tatar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A nonlinear beam equation describing the transversal vibrations of a beam with boundary feedback is considered. The boundary feedback involves a fractional derivative. We discuss the asymptotic behavior of solutions. In fact, we prove that solutions blow up in finite time under certain assumptions on the nonlinearity.

Original language	English
Pages (from-to)	1402-1409
Number of pages	8
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	74
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2010.10.012
State	Published - 15 Feb 2011

Keywords

Blow up
Boundary feedback
Fractional derivative
Non-dissipative system
Singular kernel

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2010.10.012

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@article{8a628c1cc08342858106b50607dae2e3,

title = "Blow-up of solutions for a nonlinear beam equation with fractional feedback",

abstract = "A nonlinear beam equation describing the transversal vibrations of a beam with boundary feedback is considered. The boundary feedback involves a fractional derivative. We discuss the asymptotic behavior of solutions. In fact, we prove that solutions blow up in finite time under certain assumptions on the nonlinearity.",

keywords = "Blow up, Boundary feedback, Fractional derivative, Non-dissipative system, Singular kernel",

author = "Soraya Labidi and Tatar, \{Nasser Eddine\}",

year = "2011",

month = feb,

day = "15",

doi = "10.1016/j.na.2010.10.012",

language = "English",

volume = "74",

pages = "1402--1409",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd.",

number = "4",

}

TY - JOUR

T1 - Blow-up of solutions for a nonlinear beam equation with fractional feedback

AU - Labidi, Soraya

AU - Tatar, Nasser Eddine

PY - 2011/2/15

Y1 - 2011/2/15

N2 - A nonlinear beam equation describing the transversal vibrations of a beam with boundary feedback is considered. The boundary feedback involves a fractional derivative. We discuss the asymptotic behavior of solutions. In fact, we prove that solutions blow up in finite time under certain assumptions on the nonlinearity.

AB - A nonlinear beam equation describing the transversal vibrations of a beam with boundary feedback is considered. The boundary feedback involves a fractional derivative. We discuss the asymptotic behavior of solutions. In fact, we prove that solutions blow up in finite time under certain assumptions on the nonlinearity.

KW - Blow up

KW - Boundary feedback

KW - Fractional derivative

KW - Non-dissipative system

KW - Singular kernel

UR - https://www.scopus.com/pages/publications/78650516125

U2 - 10.1016/j.na.2010.10.012

DO - 10.1016/j.na.2010.10.012

M3 - Article

AN - SCOPUS:78650516125

SN - 0362-546X

VL - 74

SP - 1402

EP - 1409

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 4

ER -

Blow-up of solutions for a nonlinear beam equation with fractional feedback

Abstract

Keywords

ASJC Scopus subject areas

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