On the dynamics of deformable ferromagnets i. global weak solutions for soft ferromagnets at rest

Annali di Matematica Pura ed Applicata

Volumn 179, Issue 1, 2001, Pages 331-360

  Bertsch, M ^a   Podio Guidugli, P ^a   Valente, V ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b CNR   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013199304     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF02505962     Document Type: Article

References (32)

1. F. ALOUGES - A. SOYEUR, On global weak solutions for Landau-Lifshitz équations: existence and nonuniqueness, Nonlinear Anal. Theory, Meth. Appl., 18 (1992), pp. 1071-1084.
2. S. S. ANTMAN, Nonlinear Problems of Elasticity, Springer-Verlag (1995).
3. G. ANZELLOTTI - S. BALDO - A. VISLNTIN, Asymptotic behavior of the Landau-Lifshitz model offerromagnetism, Appl. Math. Optim., 23 (1991), pp. 171-192.
4. M. BERTSCH - R. DAL PASSO - R. VAN DER Hour, Nonuniqueness for the heat flow of harmonic maps on the disk, preprint (1999).
5. F. BETHUEL - J. M. CORON - J. M. GmoAGUA - A. SOYEUR, Heat flows and relaxed energies for har-monic maps, in: Nonlinear Diffusion Equations and their Equilibrium States (N. G. Lloyd, W. N. Ni, L. A. Peletier, J. Serrin, Ed.), pp. 99-109, Gregynog, Birkhauser (1990).
6. H. BREZIS - J. M. CORON - E. H. LIEB, Harmonic maps with defects, Commun. Math. Phys, 107 (1986), pp. 649-705.
7. W. F. BROWN, Magnetoelastic Interactions, Springer-Verlag (1966).
8. W. F. BROWN, Micromagnetics, Krieger, 1978.
9. K. C. CHANG - W. Y. DING - R. YE, Finite-time blow-up of the heat flow of harmonic maps from sur-faces, J. Differential Geometry, 36 (1992), pp. 507-515.
10. Y. CHEN - M. STRUWE, Existence and partial regularity results for the heat flow for harmonic maps, Math. Z., 201 (1989), pp. 83-103.
11. J. M. CORON, Nonuniqueness for the heat flow of harmonic maps, Ann. Inst. Henri Poincaré, 7 (1990), pp. 335-344.
12. R. DAL PASSO - E. ViLUcan, in preparation (1999).
13. A. DE SLMONE - P. PODIO GUIDUGLI, Inertial and self interactions in structured continua: liquid crys-tals and magnetostrictive solids, MECCANICA, 30 (1995), pp. 629-640.
14. A. DE SIMONE - P. PODIO GUIDUGLI, On the continuum theory of deformable ferromagnetic solids, Arch. Rational Mech. Anal, 136 (1996), pp. 201-233.
15. A. DE SLMONE - P. PODIO GUIDUGLI, Pointwise balances and the construction of stress fields in dielectrics, Math. Models Methods Appl. Sci., 7 (1997), pp. 447- 485.
16. A. FRETRE, Uniqueness for the harmonic map flow from surfaces to general targets, Comment. Math. Helv., 70 (1995), pp. 310-338.
17. B. Guo - M. C. HONG, The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps, Cal. Var., 1 (1993), pp. 311-334.
18. M. E. GURTLM, Thermomechanics of Evolving Phase Boundaries in the Plane, Clarendon Press, 1993.
19. M. E. GURTLN - P. W. VOORHEES, The continuum mechanics of two-phase elastic solids with mass transport, Proc. Roy. Soc. London A, 440 (1993), pp. 323-343.
20. R. M. HARDT, Singularities of harmonic maps, Bull. Amer. Math. Soc., 34 (1997), pp. 15-34.
21. M. C. HONG, Some new examples for nonuniqueness of the evolution problem of harmonic maps, Comm. Anal. Geom., 6 (1998), pp. 779-787.
22. R. D. JAMES - D. KINDERLEHRER, Frustration in ferromagnetic materials, Cont. Mech. Therm., 2 (1990), pp. 215-239.
23. M. LAKSHMANAN - K. NAKAMURA, Landau-Lifskitz equation of ferromagnetism: exact treatment of the Gilbert Damping, Phys. Rev. Letters, 53 (1984), pp. 2497-2499.
24. L. LANDAU - E. LISHITZ, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Phys. Z. Sowjet., 8 (1935), pp. 153, Reprinted on; pp. 101-114 of Collected Papers of L. D. Landau (D. ter Haar, Ed.), Pergamon Press (1965).
25. P. PODIO GUIDUGLI, Inertia and invariance, Ann. Mat. Pura Appl., 172 (1997), pp. 103-124.
26. M. STRUWE, Geometric evolution problems of Nonlinear Partial Differential Equations in Differ-ential Geometry, IAS Park City Math. Sen, Vol. 2, Am. Math. Soc. (1996), pp. 257-339.
27. R. VAN DER Hour, Flow alignment in nematic liquid crystals in flows with cylindrical symmetry (1997), to appear.
28. E. ViLUCcm, An existence theorem for soft ferromagnets subject to magnetic actions, IAC/C.N.R., Quad. 16/1997.
29. A. VISINTIN, On Landau-Lifshitz' equations for ferromagnetism, Japan]. Appl. Math., 2 (1985), pp. 69-84.
30. A. VISINTIN, Modified Landau-Lifshitz equation for ferromagnetism, Physica B, 233 (1997), pp. 365-369
31. [MS] S. MüLLER - M. STRUKT, Global existence of wave maps in 1+2 dimensions with finite energy data, Topol. Meth. Nonlinear Analysis, 7 (1996), pp. 245-259.
32. [Z] Y. ZHOU, Global weak solutions for 1+2 dimensional wave maps into homogeneous spaces, preprint, 1995.