Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation

Soraya Labidi; Nasser Eddine Tatar

doi:10.1016/j.amc.2003.12.057

Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation

Soraya Labidi^*, Nasser Eddine Tatar

^*Corresponding author for this work

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

15 Scopus citations

Abstract

We consider the Euler-Bernoulli beam problem with some boundary controls involving a fractional derivative. The fractional derivative here represents a fractional dissipation of lower order than one. We prove that the classical energy associated to the system is unbounded in presence of a polynomial nonlinearity. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity.

Original language	English
Pages (from-to)	697-706
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	161
Issue number	3
DOIs	https://doi.org/10.1016/j.amc.2003.12.057
State	Published - 2005

Keywords

Euler-Bernoulli beam equation
Exponential growth
Fourier transforms
Fractional derivative
Hardy-Littlewood-Sobolev inequality

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2003.12.057

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title = "Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation",

abstract = "We consider the Euler-Bernoulli beam problem with some boundary controls involving a fractional derivative. The fractional derivative here represents a fractional dissipation of lower order than one. We prove that the classical energy associated to the system is unbounded in presence of a polynomial nonlinearity. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity.",

keywords = "Euler-Bernoulli beam equation, Exponential growth, Fourier transforms, Fractional derivative, Hardy-Littlewood-Sobolev inequality",

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

year = "2005",

doi = "10.1016/j.amc.2003.12.057",

language = "English",

volume = "161",

pages = "697--706",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

number = "3",

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TY - JOUR

T1 - Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation

AU - Labidi, Soraya

AU - Tatar, Nasser Eddine

PY - 2005

Y1 - 2005

N2 - We consider the Euler-Bernoulli beam problem with some boundary controls involving a fractional derivative. The fractional derivative here represents a fractional dissipation of lower order than one. We prove that the classical energy associated to the system is unbounded in presence of a polynomial nonlinearity. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity.

AB - We consider the Euler-Bernoulli beam problem with some boundary controls involving a fractional derivative. The fractional derivative here represents a fractional dissipation of lower order than one. We prove that the classical energy associated to the system is unbounded in presence of a polynomial nonlinearity. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity.

KW - Euler-Bernoulli beam equation

KW - Exponential growth

KW - Fourier transforms

KW - Fractional derivative

KW - Hardy-Littlewood-Sobolev inequality

UR - https://www.scopus.com/pages/publications/10644286405

U2 - 10.1016/j.amc.2003.12.057

DO - 10.1016/j.amc.2003.12.057

M3 - Article

AN - SCOPUS:10644286405

SN - 0096-3003

VL - 161

SP - 697

EP - 706

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 3

ER -

Unboundedness for the Euler-Bernoulli beam equation with a fractional boundary dissipation

Abstract

Keywords

ASJC Scopus subject areas

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