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- Michael A. Zaks, Alla Podolny, Alexander A. Nepomnyashchy, Alexander A. Golovin
- SIAM Journal of Applied Mathematics
- 2005

We investigate bifurcations of stationary periodic solutions of a convective Cahn– Hilliard equation, ut+Duux+(u−u+uxx)xx = 0, describing phase separation in driven systems, and study the stability of the main family of these solutions. For the driving parameter D < D0 = √ 2/3, the periodic stationary solutions are unstable. For D > D0, the periodic… (More)

The convective Cahn–Hilliard (CCH) equation, ut + (uxx + u− u)xx − (D/2)(u)x = 0, has been suggested recently for the description of several physical phenomena, including spinodal decomposition of (driven) phase separating systems in an external field, instability of steps moving on a crystal surface, and faceting of growing, thermodynamically unstable… (More)

- A Podolny, A A Nepomnyashchy, A Oron
- Physical review. E, Statistical, nonlinear, and…
- 2007

We consider a system which consists of a layer of an incompressible binary liquid with a deformable free surface, and a thick solid substrate subjected to a differential heating across it. We investigate the long-wave thermosolutal Marangoni instability in the case of asymptotically small Lewis and Galileo numbers for finite capillary and Biot numbers with… (More)

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