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Existence and asymptotic behavior for a convection problem
Journal article   Peer reviewed

Existence and asymptotic behavior for a convection problem

Khaled M. Furati, Mokhtar Kirane and Nasser-eddine Tatar
Nonlinear analysis, Vol.59(3), pp.407-424
01/11/2004
DOI: https://doi.org/10.1016/j.na.2004.07.021

Abstract

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

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