Existence and asymptotic behavior for a convection problem

Khaled M. Furati; Mokhtar Kirane; Nasser Eddine Tatar

doi:10.1016/j.na.2004.07.021

Existence and asymptotic behavior for a convection problem

Khaled M. Furati, Mokhtar Kirane, Nasser Eddine Tatar^*

^*Corresponding author for this work

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

4 Scopus citations

Abstract

We prove global existence and exponential decay of solutions for a system which arise in thermal convection flow. For sufficiently small initial data, these results improve previous ones in (Funkcial. Ekvac. 34 (1991) 449). Further, we investigate the behavior of solutions for arbitrarily large initial data. In particular, we show that the length of the interval on which we have existence and exponential decay is inverse proportional to the size of the initial data.

Original language	English
Pages (from-to)	407-424
Number of pages	18
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	59
Issue number	3
DOIs	https://doi.org/10.1016/j.na.2004.07.021
State	Published - Nov 2004

Bibliographical note

Funding Information:
The first and third authors would like to express their gratitude to King Fahd University for the facilities provided and the financial support.

Keywords

Asymptotic behavior
Exponential decay
Global existence
Gronwall-Bihari type inequality
Nonstationary convection problem
Semi-group theory

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2004.07.021

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title = "Existence and asymptotic behavior for a convection problem",

abstract = "We prove global existence and exponential decay of solutions for a system which arise in thermal convection flow. For sufficiently small initial data, these results improve previous ones in (Funkcial. Ekvac. 34 (1991) 449). Further, we investigate the behavior of solutions for arbitrarily large initial data. In particular, we show that the length of the interval on which we have existence and exponential decay is inverse proportional to the size of the initial data.",

keywords = "Asymptotic behavior, Exponential decay, Global existence, Gronwall-Bihari type inequality, Nonstationary convection problem, Semi-group theory",

author = "Furati, \{Khaled M.\} and Mokhtar Kirane and Tatar, \{Nasser Eddine\}",

note = "Funding Information: The first and third authors would like to express their gratitude to King Fahd University for the facilities provided and the financial support.",

year = "2004",

month = nov,

doi = "10.1016/j.na.2004.07.021",

language = "English",

volume = "59",

pages = "407--424",

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

issn = "0362-546X",

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TY - JOUR

T1 - Existence and asymptotic behavior for a convection problem

AU - Furati, Khaled M.

AU - Kirane, Mokhtar

AU - Tatar, Nasser Eddine

N1 - Funding Information: The first and third authors would like to express their gratitude to King Fahd University for the facilities provided and the financial support.

PY - 2004/11

Y1 - 2004/11

N2 - We prove global existence and exponential decay of solutions for a system which arise in thermal convection flow. For sufficiently small initial data, these results improve previous ones in (Funkcial. Ekvac. 34 (1991) 449). Further, we investigate the behavior of solutions for arbitrarily large initial data. In particular, we show that the length of the interval on which we have existence and exponential decay is inverse proportional to the size of the initial data.

AB - We prove global existence and exponential decay of solutions for a system which arise in thermal convection flow. For sufficiently small initial data, these results improve previous ones in (Funkcial. Ekvac. 34 (1991) 449). Further, we investigate the behavior of solutions for arbitrarily large initial data. In particular, we show that the length of the interval on which we have existence and exponential decay is inverse proportional to the size of the initial data.

KW - Asymptotic behavior

KW - Exponential decay

KW - Global existence

KW - Gronwall-Bihari type inequality

KW - Nonstationary convection problem

KW - Semi-group theory

UR - https://www.scopus.com/pages/publications/4944220082

U2 - 10.1016/j.na.2004.07.021

DO - 10.1016/j.na.2004.07.021

M3 - Article

AN - SCOPUS:4944220082

SN - 0362-546X

VL - 59

SP - 407

EP - 424

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 3

ER -

Existence and asymptotic behavior for a convection problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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