On a boundary controller of fractional type

Nasser eddine Tatar

doi:10.1016/j.na.2009.12.017

On a boundary controller of fractional type

Nasser eddine Tatar^*

^*Corresponding author for this work

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

6 Scopus citations

Abstract

In this paper we consider the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. The boundary controller involves a derivative of non-integer order. It is proved that solutions blow up in finite time in the presence of a nonlinear source.

Original language	English
Pages (from-to)	3209-3215
Number of pages	7
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	72
Issue number	6
DOIs	https://doi.org/10.1016/j.na.2009.12.017
State	Published - 15 May 2009

Bibliographical note

Funding Information:
The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals.

Keywords

Blow up in finite time
Boundary control
Concavity method
Fractional derivative
Wave equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2009.12.017

Cite this

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title = "On a boundary controller of fractional type",

abstract = "In this paper we consider the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. The boundary controller involves a derivative of non-integer order. It is proved that solutions blow up in finite time in the presence of a nonlinear source.",

keywords = "Blow up in finite time, Boundary control, Concavity method, Fractional derivative, Wave equation",

author = "Tatar, \{Nasser eddine\}",

note = "Funding Information: The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals.",

year = "2009",

month = may,

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doi = "10.1016/j.na.2009.12.017",

language = "English",

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

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T1 - On a boundary controller of fractional type

AU - Tatar, Nasser eddine

N1 - Funding Information: The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals.

PY - 2009/5/15

Y1 - 2009/5/15

N2 - In this paper we consider the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. The boundary controller involves a derivative of non-integer order. It is proved that solutions blow up in finite time in the presence of a nonlinear source.

AB - In this paper we consider the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. The boundary controller involves a derivative of non-integer order. It is proved that solutions blow up in finite time in the presence of a nonlinear source.

KW - Blow up in finite time

KW - Boundary control

KW - Concavity method

KW - Fractional derivative

KW - Wave equation

UR - https://www.scopus.com/pages/publications/73249114916

U2 - 10.1016/j.na.2009.12.017

DO - 10.1016/j.na.2009.12.017

M3 - Article

AN - SCOPUS:73249114916

SN - 0362-546X

VL - 72

SP - 3209

EP - 3215

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 6

ER -

On a boundary controller of fractional type

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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