Exponential growth for a fractionally damped wave equation

M. Kirane; N. E. Tatar

doi:10.4171/zaa/1137

Exponential growth for a fractionally damped wave equation

M. Kirane^*, N. E. Tatar

^*Corresponding author for this work

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

40 Scopus citations

Abstract

We consider a nonlinear wave equation with an internal damping represented by a fractional time derivative and with a polynomial source. It is proved that the solution is unbounded and grows up exponentially in the L_p-norm for sufficiently large initial data. To this end we use some techniques based on Fourier transforms and some inequalities such as the Hardy-Littlewood inequality.

Original language	English
Pages (from-to)	167-177
Number of pages	11
Journal	Zeitschrift fur Analysis und ihre Anwendung
Volume	22
Issue number	1
DOIs	https://doi.org/10.4171/zaa/1137
State	Published - 2003

Keywords

Exponential growth
Fractional derivative
Internal damping

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.4171/zaa/1137

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title = "Exponential growth for a fractionally damped wave equation",

abstract = "We consider a nonlinear wave equation with an internal damping represented by a fractional time derivative and with a polynomial source. It is proved that the solution is unbounded and grows up exponentially in the Lp-norm for sufficiently large initial data. To this end we use some techniques based on Fourier transforms and some inequalities such as the Hardy-Littlewood inequality.",

keywords = "Exponential growth, Fractional derivative, Internal damping",

author = "M. Kirane and Tatar, \{N. E.\}",

year = "2003",

doi = "10.4171/zaa/1137",

language = "English",

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pages = "167--177",

journal = "Zeitschrift fur Analysis und ihre Anwendung",

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TY - JOUR

T1 - Exponential growth for a fractionally damped wave equation

AU - Kirane, M.

AU - Tatar, N. E.

PY - 2003

Y1 - 2003

N2 - We consider a nonlinear wave equation with an internal damping represented by a fractional time derivative and with a polynomial source. It is proved that the solution is unbounded and grows up exponentially in the Lp-norm for sufficiently large initial data. To this end we use some techniques based on Fourier transforms and some inequalities such as the Hardy-Littlewood inequality.

AB - We consider a nonlinear wave equation with an internal damping represented by a fractional time derivative and with a polynomial source. It is proved that the solution is unbounded and grows up exponentially in the Lp-norm for sufficiently large initial data. To this end we use some techniques based on Fourier transforms and some inequalities such as the Hardy-Littlewood inequality.

KW - Exponential growth

KW - Fractional derivative

KW - Internal damping

UR - https://www.scopus.com/pages/publications/0037229854

U2 - 10.4171/zaa/1137

DO - 10.4171/zaa/1137

M3 - Article

AN - SCOPUS:0037229854

SN - 0232-2064

VL - 22

SP - 167

EP - 177

JO - Zeitschrift fur Analysis und ihre Anwendung

JF - Zeitschrift fur Analysis und ihre Anwendung

IS - 1

ER -

Exponential growth for a fractionally damped wave equation

Abstract

Keywords

ASJC Scopus subject areas

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