Publication Cover
Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 7
34
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Initial-boundary value problem for higher dimensional landau–lifshitz systems

&
Pages 673-697 | Received 01 Aug 2003, Published online: 15 Aug 2006

References

  • Alouges F Soyeur A 1992 On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness Nonlinear Analysis TMA 18 11 1084
  • Chen , Y . 1991 . Dirichlet problem for heat flows of harmonic maps in higher dimensions . Math. Z. , 208 : 557 – 565 .
  • Chen , Y . 2000 . Dirichlet boundary value problems for Landau-Lifshitz equations . Comm. Partial Differential Equations , 25 ( 1–2 ) : 101 – 124 .
  • Chen Y 2002 Existence and singularities for Dirichlet boundary value problems of Landau-Lifshitz equations Nonlinear Analysis TMA 48 411 426
  • Cheng , X . 1991 . Estimate of the singular set of the evolution problem for harmonic maps . J. Diff. Geom. , 34 : 169 – 174 .
  • Chen , Y , Ding , S and Guo , B . 1998 . Partial regularity for two-dimensional Landau-Lifshitz equations . Acta Math. Sinica , 14 ( 3 ) : 423 – 432 .
  • Chen , Y and Lin , FH . 1993 . Evolution of harmonic maps with Dirichlet boundary conditions . Comm. Anal. Geom. , 1 : 327 – 346 .
  • Chen , Y , Li , J and Lin , FH . 1995 . Partial regularity for weak heat flows into spheres . Comm. Pure Appl. Math. , XLVIII : 429 – 448 .
  • Chen , Y and Struwe , M . 1989 . Existence and partial regularity results for the heat flow of harmonic maps . Math. Z. , 201 : 83 – 103 .
  • Chen , Y and Wang , C . 1996 . Partial regularity for weak flows into Riemannian homogeneous space . Comm. P. D. E. , 21 ( 5–6 ) : 735 – 761 .
  • Eidel'man SD 1969 Parabolic Systems, North-Holland Groningen Noordhoft, Amsterdam, London
  • Coron , J . 1990 . Nonuniqueness for the heat flow of harmonic maps . Ann. Inst. H. Poincaré, Non-Linéairé , 7 : 335 – 344 .
  • Ding , S and Guo , B . 2000 . Initial-boundary value problem for the unsaturated Landau-Lifshitz system of ferromagnetic spin chain . Chinese Ann. Math. , 21B : 389 – 402 .
  • Ding S Guo B 2002 Partial Regularity for Higher Dimensional Landau-Lifshitz Systems (Preprint)
  • Feldman , M . 1994 . Partial regularity for harmonic maps of evolution into spheres . Comm. PDE. , 19 : 761 – 790 .
  • Freir , A . 1996 . Uniqueness for the harmonic heat flow in two dimensions . Calc. Var. PDE. , 4 : 761 – 790 .
  • Guo B Ding S 1998 Initial-boundary value problem for the Landau-Lifshitz systems of ferromagnetic spin chain Progress Nat. Sci. 8 1 11 23 ; 8(2), 147–151
  • Guo , B and Hong , M . 1993 . The Landau-Lifshitz equations of the ferromagnetic spin chain and harmonic maps . Calc. Var. PDE. , 1 : 311 – 334 .
  • Guo , B and Wang , Y . 1996 . Generalized Landau-Lifshitz systems of ferromagnetic spin chain type and harmonic maps . Science in China , 26 ( A ) : 800 – 810 .
  • Liu X 2001 Partial regularity for Landau-Lifshitz system of ferromagnetic spin chain (Preprint)
  • Riviére , T . 1992 . Everywhere discontinuous harmonic maps from B 3 into S 2 . C. R. Acad. Sci. Paris , 314 : 719 – 723 .
  • Simon L 1983 Lectures on Geometric Measure Theory, Australian National Univ. Press
  • Stromberg J Torchinsky A 1989 Weighted Hardy Spaces Lecture Notes in Math. No.1381
  • Zhou , Y and Guo , B . 1984 . Existence of weak solution for boundary problems of systems of ferromagnetic chain . Science in China , A27 : 799 – 811 .
  • Zhou , Y and Guo , B . 1987 . Weak solution systems of ferromagnetic chain with several variables . Science in China , A30 : 1251 – 1266 .
  • Zhou , Y , Guo , B and Tan , S . 1991 . Existence and uniqueness of smooth solution of system of ferromagnetic chain . Science in China , A34 : 257 – 266 .
  • Zhou , Y , Sun , H and Guo , B . 1993 . Multidimensional system of ferromagnetic chain type . Science in China , A36 : 1422 – 1434 .
  • Zhou , Y , Sun , H and Guo , B . 1993 . Cauchy problem for system of ferromagnetic chain type . Science in China , A36 : 927 – 939 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.