Blow up for the wave equation with a fractional damping

M. R. Alaimia; N. E. Tatar

doi:10.1515/JAA.2005.133

Blow up for the wave equation with a fractional damping

M. R. Alaimia^*, N. E. Tatar

^*Corresponding author for this work

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

15 Scopus citations

Abstract

We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time.

Original language	English
Pages (from-to)	133-144
Number of pages	12
Journal	Journal of Applied Analysis
Volume	11
Issue number	1
DOIs	https://doi.org/10.1515/JAA.2005.133
State	Published - Jun 2005

Bibliographical note

Funding Information:
2000 Mathematics Subject Classification. 35L20, 35L70, 35B05. Key words and phrases. Blow up, Caputo’s fractional derivative, integro-differential problem, modified energy functional, singular kernel. The authors are very grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals. This work has been supported by the SABIC/FAST TRACK (Saudi Arabia) for scientific research under the grant No FT/2003-10.

Keywords

Blow up
Caputo's fractional derivative
Integro-differential problem
Modified energy functional
Singular kernel

ASJC Scopus subject areas

Mathematical Physics
Statistics, Probability and Uncertainty
Computational Theory and Mathematics
Applied Mathematics

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10.1515/JAA.2005.133

Cite this

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title = "Blow up for the wave equation with a fractional damping",

abstract = "We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time.",

keywords = "Blow up, Caputo's fractional derivative, Integro-differential problem, Modified energy functional, Singular kernel",

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

note = "Funding Information: 2000 Mathematics Subject Classification. 35L20, 35L70, 35B05. Key words and phrases. Blow up, Caputo{\textquoteright}s fractional derivative, integro-differential problem, modified energy functional, singular kernel. The authors are very grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals. This work has been supported by the SABIC/FAST TRACK (Saudi Arabia) for scientific research under the grant No FT/2003-10.",

year = "2005",

month = jun,

doi = "10.1515/JAA.2005.133",

language = "English",

volume = "11",

pages = "133--144",

journal = "Journal of Applied Analysis",

issn = "1425-6908",

publisher = "Walter de Gruyter GmbH",

number = "1",

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TY - JOUR

T1 - Blow up for the wave equation with a fractional damping

AU - Alaimia, M. R.

AU - Tatar, N. E.

N1 - Funding Information: 2000 Mathematics Subject Classification. 35L20, 35L70, 35B05. Key words and phrases. Blow up, Caputo’s fractional derivative, integro-differential problem, modified energy functional, singular kernel. The authors are very grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals. This work has been supported by the SABIC/FAST TRACK (Saudi Arabia) for scientific research under the grant No FT/2003-10.

PY - 2005/6

Y1 - 2005/6

N2 - We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time.

AB - We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time.

KW - Blow up

KW - Caputo's fractional derivative

KW - Integro-differential problem

KW - Modified energy functional

KW - Singular kernel

UR - https://www.scopus.com/pages/publications/34248208464

U2 - 10.1515/JAA.2005.133

DO - 10.1515/JAA.2005.133

M3 - Article

AN - SCOPUS:34248208464

SN - 1425-6908

VL - 11

SP - 133

EP - 144

JO - Journal of Applied Analysis

JF - Journal of Applied Analysis

IS - 1

ER -

Blow up for the wave equation with a fractional damping

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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