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# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Asymptotic dynamics in double-diffusive convection

### Tom 35 / 2008

Applicationes Mathematicae 35 (2008), 223-245 MSC: 35B, 35Q, 37L, 76R. DOI: 10.4064/am35-2-7

#### Streszczenie

We consider the double-diffusive convection phenomenon and analyze the governing equations. A system of partial differential equations describing the convective flow arising when a layer of fluid with a dissolved solute is heated from below is considered. The problem is placed in a functional analytic setting in order to prove a theorem on existence, uniqueness and continuous dependence on initial data of weak solutions in the class $\mathcal{C}([0,\infty); H) \cap L^2_{\rm loc}(\mathbb{R}^+;V)$. This theorem enables us to show that the infinite-dimensional dynamical system generated by the double-diffusive convection equations has a global attractor on which the long-term dynamics of solutions is focused.

#### Autorzy

• Miko/laj PiniewskiInstitute of Applied Mathematics
and Mechanics
University of Warsaw
Banacha 2
02-097 Warszawa, Poland
and
Department of Hydraulic Engineering
and Environmental Restoration
Warsaw University of Life Sciences
Nowoursynowska 159
02-787 Warszawa, Poland
e-mail

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