Asymptotic behavior of thin ferroelectric materials.
Asymptotics of time harmonic solutions to a thin ferroelectric model.
Homogenization of ferromagnetic multilayers in the presence of surface energies
We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is...
Le equazioni di evoluzione dei continui ferromagnetici
This expository paper is meant to be a faithful account the invited lecture I gave in Naples on September 14, 1999, during the 16th Congress of U.M.I., the Italian Mathematical Union. In Section 2, I consider the Gilbert equation, the parabolic equation that rules the evolution of the magnetization vector in a rigid ferromagnet. Among the issues I here discuss are the relations of the Gilbert equation to the harmonic map equation and its heat flow, the existence of global-in-time weak solutions,...
Magnetic and superconductive states in the repulsive Hubbard model
On Cauchy problem for the equations of reactor kinetics.
In this paper, the initial value problem for the equations of reactor kinetics is solved and the temperature feedback is taken into account. The space where the problem is solved is chosen in such a way that it may correspond best of all to the mathematical properties of the cross-section models. The local solution is found by the method of iterations, its uniqueness is proved and it is shown also that existence of global solution is ensured in the most cases. Finally, the problem of mild solution...
The algebraic Bethe Ansatz and vacuum vectors.
О необходимых условиях оптимальности в одной задаче оптимального управления процессом тепло- и массопереноса
Развитие и применение метода численного статистического моделирования для решения многомерных задач теории переноса излучения
Сверхпроводящие состояния в двумерной модели Хаббарда с отталкиванием
Теория возмущений для основного синглетного состояния гейзенберговской антиферромагнитной цепочки спинов 1/2