caa a22 4500 445843756 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00526-010-0377-4 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0377-4 The fractional Landau-Lifshitz-Gilbert equation and the heat flow of harmonic maps [Elektronische Daten] [Xueke Pu, Boling Guo] In this paper, we prove the existence of global weak solutions to the periodic fractional Landau-Lifshitz-Gilbert equation through the Ginzburg-Landau approximation and the Galerkin approximation. Since the nonlinear term is nonlocal and of full order of the equation, some special structures of the equation, the commutator estimate and some calculus inequalities of fractional order are exploited to get the convergence of the approximating solutions. The equation considered in this paper can also be regarded as a generalization of the heat flow of harmonic maps to the fractional order. Springer-Verlag, 2010 Pu Xueke College of Mathematics and Statistics, Chongqing University, 401331, Chongqing, People's Republic of China aut Guo Boling Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, 100088, Beijing, People's Republic of China aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/1-2(2011-09-01), 1-19 0944-2669 42:1-2<1 2011 42 526 https://doi.org/10.1007/s00526-010-0377-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0377-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pu Xueke College of Mathematics and Statistics, Chongqing University, 401331, Chongqing, People's Republic of China aut NATIONALLICENCE 700 1- Guo Boling Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, 100088, Beijing, People's Republic of China aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/1-2(2011-09-01), 1-19 0944-2669 42:1-2<1 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer