This article is cited in 3 papers

Differentical equations, dynamical systems and optimal control

Special case of the Cahn-Hilliard Equation

O. A. Frolovskaya^ab, O. V. Admaev^c, V. V. Pukhnachev<sup>ab

a</sup> Lavrentyev Institute of Hydrodynamics SB RAS, pr. Lavrentieva, 15
^b Novosibirsk State University, Pirogova str., 2, 630090, Novosibirsk, Russia
^c Krasnoyarsk Institute of Railway Engineering, Branch of Irkutsk State Transport University, Lado Ketskhoveli str., 89, 660028, Krasnoyarsk, Russia

Abstract: A qualitative behaviour of the Cauchy problem solution for the Cahn–Hilliard kind equation is analyzed. The sufficient condition of the global solution existence and its collapse for a finite time for the periodic function has been formulated. The examples of the stationary, self-similar and collapsing solutions are constructed.

Keywords: Cahn–Hilliard Equation, Cauchy problem, Lyapunov functional, similarity solutions.

UDC: 517.9

MSC: 35B07, 35B10, 35B44

Received February 15, 2013, published April 10, 2013

Language: English