O. A. Frolovskaya, O. V. Admaev, V. V. Pukhnachev, “Special case of the Cahn-Hilliard Equation”, Сиб. электрон. матем. изв., 2013, том 10,страницы 324

Эта публикация цитируется в 3 статьях

Дифференциальные уравнения, динамические системы и оптимальное управление

Special case of the Cahn-Hilliard Equation

O. A. Frolovskaya^ab, O. V. Admaev^c, V. V. Pukhnachev^ab

^a 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

Аннотация: 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.

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

УДК: 517.9

MSC: 35B07, 35B10, 35B44

Поступила 15 февраля 2013 г., опубликована 10 апреля 2013 г.

Язык публикации: английский