no. 2
Traveling wave solutions of the heat flow of director fields
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 2, pp. 227-250. 
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     title = {Traveling wave solutions of the heat flow of director fields},
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     publisher = {Elsevier},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.008/}
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Bertsch, M.; Primi, I. Traveling wave solutions of the heat flow of director fields. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 2, pp. 227-250. doi : 10.1016/j.anihpc.2006.03.008. http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.008/

[1] Bertsch M., Dal Passo R., Pisante A., Point singularities and nonuniqueness for the heat flow for harmonic maps, Comm. Partial Differential Equations 28 (2003) 1135-1160. | MR | Zbl

[2] Bertsch M., Dal Passo R., Van Der Hout R., Nonuniqueness for the heat flow of harmonic maps on the disk, Arch. Rational Mech. Anal. 161 (2) (2002) 93-112. | MR | Zbl

[3] Bertsch M., Muratov C., Primi I., Traveling wave solutions of harmonic heat flow, Calc. Var. Partial Differential Equations 26 (2006) 489-509. | MR | Zbl

[4] M. Bertsch, I. Primi, Non uniqueness of the traveling wave speed for harmonic heat flow, preprint, 2005.

[5] Bertsch M., Podio-Guidugli P., Valente V., On the dynamics of deformable ferromagnets. I. Global weak solutions for soft ferromagnets at rest, Ann. Mat. Pura Appl. CLXXIX (2001) 331-360. | MR | Zbl

[6] Bethuel F., Brezis H., Coron J.M., Relaxed energies for harmonic maps, in: Variational Methods (Paris, 1988), Progress in Nonlinear Differential Equations and their Applications, vol. 4, Birkhäuser Boston, Boston, 1990, pp. 37-52. | MR | Zbl

[7] Chang K.-C., Ding W.-Y., Ye R., Finite-time blow-up of the heat flow of harmonic maps from surfaces, J. Differential Geom. 36 (2) (1992) 507-515. | MR | Zbl

[8] Coron J.M., Nonuniqueness for the heat flow of harmonic maps, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 335-344. | Numdam | MR | Zbl

[9] Grotowski J.F., Harmonic map heat flow for axially symmetric data, Manuscripta Math. 73 (1991) 207-228. | MR | Zbl

[10] Grotowski J.F., Concentrated boundary data and axially symmetric harmonic maps, J. Geom. Anal. 3 (1993) 279-292. | MR | Zbl

[11] Hamilton R.S., Harmonic Maps of Manifolds with Boundary, Lecture Notes, vol. 471, Springer, Berlin, 1975. | MR | Zbl

[12] Hardt R., Lin F.H., Poon C.C., Axially symmetric harmonic maps minimizing a relaxed energy, Comm. Pure Appl. Math. 14 (1992) 417-459. | MR | Zbl

[13] Jost J., Harmonic mappings between Riemannian manifolds, in: Proc. Centre Math. Analysis, Canberra, Australian National University Press, 1983. | MR | Zbl

[14] Kawohl B., Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Mathematics, vol. 1150, Springer-Verlag, Berlin, 1985. | MR | Zbl

[15] I. Primi, Nonuniqueness of the heat flow of director fields, in preparation.

[16] Matano H., Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (2) (1982) 401-441. | MR | Zbl

[17] Pisante A., Reverse bubbling of currents and harmonic heat flows with prescribed singular set, Calc. Var. Partial Differential Equations 19 (4) (2004) 337-378. | MR | Zbl

[18] I. Primi, Traveling Waves of Director Fields, PhD thesis, University of Rome “La Sapienza”, 2005.

[19] Topping P., Reverse bubbling and nonuniqueness in the harmonic map flow, Int. Math. Res. Notices 10 (2002) 505-520. | MR | Zbl

[20] Van Der Hout R., Flow alignment in nematic liquid crystals in flows with cylindrical symmetry, Differential Integral Equations 14 (2) (2001) 189-211. | MR | Zbl

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