naa a22 4500 510812511 CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1134/S0081543813050076 doi (NATIONALLICENCE)springer-10.1134/S0081543813050076 Kalyakin L. Institute of Mathematics with Computing Center, Ufa Research Center of the Russian Academy of Sciences, ul. Chernyshevskogo 112, 450008, Ufa, Russia aut Analysis of the bloch equations for the nuclear magnetization model [Elektronische Daten] [L. Kalyakin] We consider a system of three ordinary first-order differential equations known in the theory of nuclear magnetism as the Bloch equations. The system contains four dimensionless parameters as coefficients. Equilibrium states and the dependence of their stability on these parameters are investigated. The possibility of the appearance of two stable equilibrium states is discovered. The equations are integrable in the absence of dissipation. For the problem with small dissipation far from equilibrium, approximate solutions are constructed by the method of averaging. Pleiades Publishing, Ltd., 2013 nonlinear equations nationallicence equilibrium nationallicence dissipation nationallicence stability nationallicence asymptotics nationallicence averaging nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 64-81 0081-5438 281<64 2013 281 11501 https://doi.org/10.1134/S0081543813050076 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813050076 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kalyakin L. Institute of Mathematics with Computing Center, Ufa Research Center of the Russian Academy of Sciences, ul. Chernyshevskogo 112, 450008, Ufa, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 64-81 0081-5438 281<64 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer