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Attractors for autonomous double‐diffusive convection systems based on Brinkman–Forchheimer equations
Author(s) -
Ôtani Mitsuharu,
Uchida Shun
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3776
Subject(s) - attractor , mathematics , bounded function , neumann boundary condition , mathematical analysis , nonlinear system , dirichlet distribution , dimension (graph theory) , boundary value problem , convection , pure mathematics , physics , mechanics , quantum mechanics
In this paper, we consider the existence of global attractor and exponential attractor for some dynamical system generated by nonlinear parabolic equations in bounded domains with the dimension N ≤4 which describe double‐diffusive convection phenomena in a porous medium. We deal with both of homogeneous Dirichlet and Neumann boundary condition cases. Especially, when Neumann condition is imposed, we need some assumptions and restrictions for the external forces and the average of initial data, since the mass conservation law holds. Copyright © 2015 John Wiley & Sons, Ltd.