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Volumn 26, Issue 4, 2006, Pages 489-509

Traveling wave solutions of harmonic heat flow

Author keywords

Bistable potential; Calculus of variations; Director field; Harmonic map; Singularity; Traveling wave

Indexed keywords


EID: 33744517061     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-006-0016-2     Document Type: Article
Times cited : (6)

References (28)
  • 1
    • 84862091890 scopus 로고
    • Traveling fronts in cylinders, annales de l'Institut henri poincaré
    • Berestycki, H., Nirenberg, L.: Traveling fronts in cylinders, Annales de l'Institut Henri Poincaré. Anal, non linéaire 9, 497-572 (1992)
    • (1992) Anal, Non Linéaire , vol.9 , pp. 497-572
    • Berestycki, H.1    Nirenberg, L.2
  • 5
    • 0036488685 scopus 로고    scopus 로고
    • Nonuniqueness for the heat flow of harmonic maps on the disk
    • Bertsch, M., Dal Passo, R., Van der Hout, R.: Nonuniqueness for the heat flow of harmonic maps on the disk. Arch. Rat. Mech. Anal. 161(2), 93-112 (2002)
    • (2002) Arch. Rat. Mech. Anal. , vol.161 , Issue.2 , pp. 93-112
    • Bertsch, M.1    Dal Passo, R.2    Van Der Hout, R.3
  • 6
    • 0013199304 scopus 로고    scopus 로고
    • On the dynamics of deformable ferromagnets. I. Global weak solutions for soft ferromagnets at rest
    • Bertsch, M., Podio-Guidugli, P., Valente, V.: On the dynamics of deformable ferromagnets. I. Global weak solutions for soft ferromagnets at rest. Ann. di Mat. Pura e Appl. CLXXIX, 331-360 (2001)
    • (2001) Ann. di Mat. Pura e Appl. , vol.179 , pp. 331-360
    • Bertsch, M.1    Podio-Guidugli, P.2    Valente, V.3
  • 8
    • 84972521494 scopus 로고
    • Finite-time blow-up of the heat flow of harmonic maps from surfaces
    • Chang, K.-C., Ding, W.-Y., Ye, R.: Finite-time blow-up of the heat flow of harmonic maps from surfaces. J. Diff. Geom. 36(2), 507-515 (1992)
    • (1992) J. Diff. Geom. , vol.36 , Issue.2 , pp. 507-515
    • Chang, K.-C.1    Ding, W.-Y.2    Ye, R.3
  • 9
    • 46149141487 scopus 로고
    • Existence of multidimensional traveling wave solutions of an initial-boundary value problem
    • Gardner, R., Existence of multidimensional traveling wave solutions of an initial-boundary value problem. J. Differ. Eqs. 61, 335-379 (1986)
    • (1986) J. Differ. Eqs. , vol.61 , pp. 335-379
    • Gardner, R.1
  • 10
    • 51249175910 scopus 로고
    • Harmonic map heat flow for axially symmetric data
    • Grotowski, J.F.: Harmonic map heat flow for axially symmetric data. Manuscripta Math. 73, 207-228 (1991)
    • (1991) Manuscripta Math. , vol.73 , pp. 207-228
    • Grotowski, J.F.1
  • 11
    • 0010031018 scopus 로고
    • Concentrated boundary data and axially symmetric harmonic maps
    • Grotowski, J.F.: Concentrated boundary data and axially symmetric harmonic maps. J. Geom. Anal. 3(3), 279-292 (1993)
    • (1993) J. Geom. Anal. , vol.3 , Issue.3 , pp. 279-292
    • Grotowski, J.F.1
  • 12
    • 0003234307 scopus 로고
    • Harmonic maps of manifolds with boundary
    • Berlin-Heidelberg-New York, Springer
    • Hamilton, R.S.: Harmonic Maps of Manifolds with Boundary. Lecture Notes 471, Berlin-Heidelberg-New York, Springer (1975)
    • (1975) Lecture Notes , vol.471
    • Hamilton, R.S.1
  • 13
    • 84990599123 scopus 로고
    • Axially symmetric harmonic maps minimizing a relaxed energy
    • Hardt, R., Lin, F.H., Poon, C.C.: Axially symmetric harmonic maps minimizing a relaxed energy. Commun. Pure and Appl. Math. 14, 417-459 (1992)
    • (1992) Commun. Pure and Appl. Math. , vol.14 , pp. 417-459
    • Hardt, R.1    Lin, F.H.2    Poon, C.C.3
  • 14
    • 0343271304 scopus 로고    scopus 로고
    • Preprint No. 85/2001, Max Planck Institute for Mathematics in the Sciences, Leipzig
    • Heinze, S.: A variational approach to traveling waves. Preprint No. 85/2001, Max Planck Institute for Mathematics in the Sciences, Leipzig (2001)
    • (2001) A Variational Approach to Traveling Waves
    • Heinze, S.1
  • 15
    • 0009902140 scopus 로고
    • Harmonic mappings between Riemannian manifolds
    • Canberra, Australian National University Press
    • Jost, J.: Harmonic mappings between Riemannian manifolds. In: Proceedings of the Centre Math. Analysis. Canberra, Australian National University Press (1983)
    • (1983) Proceedings of the Centre Math. Analysis
    • Jost, J.1
  • 16
    • 0003269816 scopus 로고
    • Rearrangements and convexity of level sets in PDE
    • Berlin-Heidelberg-New York, Springer-Verlag
    • Kawohl, B.: Rearrangements and Convexity of Level Sets in PDE. Lecture Notes in Mathematics 1150 Berlin-Heidelberg-New York, Springer-Verlag (1985)
    • (1985) Lecture Notes in Mathematics , vol.1150
    • Kawohl, B.1
  • 19
    • 2442629430 scopus 로고    scopus 로고
    • Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium
    • Lucia, M., Muratov, C.B., Novaga, M.: Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium. Commun. Pure Appl. Math. 57, 616-636 (2004)
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 616-636
    • Lucia, M.1    Muratov, C.B.2    Novaga, M.3
  • 20
    • 4944241607 scopus 로고    scopus 로고
    • A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type
    • Muratov, C.B.: A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type. Discrete Cont. Dyn. S., Ser. B 4, 867-892 (2004)
    • (2004) Discrete Cont. Dyn. S., Ser. B , vol.4 , pp. 867-892
    • Muratov, C.B.1
  • 21
    • 0000657925 scopus 로고
    • Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation
    • 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), 401-441 (1982)
    • (1982) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.29 , Issue.2 , pp. 401-441
    • Matano, H.1
  • 22
    • 1642602821 scopus 로고    scopus 로고
    • Reverse bubbling of currents and harmonic heat flows with prescribed singular set
    • Pisante, A.: Reverse bubbling of currents and harmonic heat flows with prescribed singular set. Calculus of Variations and Partial Differential Equations 19(4), 337-378 (2004)
    • (2004) Calculus of Variations and Partial Differential Equations , vol.19 , Issue.4 , pp. 337-378
    • Pisante, A.1
  • 24
    • 0002341651 scopus 로고    scopus 로고
    • Geometric evolution problems, Nonlinear partial differential equations in differential geometry
    • Park City, UT, 1992, AMS, Providence
    • Struwe, M.: Geometric evolution problems, Nonlinear partial differential equations in differential geometry (Park City, UT, 1992), 257-339. IAS/Park City Math. Ser., 2, AMS, Providence (1996)
    • (1996) IAS/Park City Math. Ser. , vol.2 , pp. 257-339
    • Struwe, M.1
  • 25
    • 0036350765 scopus 로고    scopus 로고
    • Reverse bubbling and nonuniqueness in the harmonic map flow
    • Topping, P.: Reverse bubbling and nonuniqueness in the harmonic map flow. Int. Math. Res. Notices 10, 505-520 (2002)
    • (2002) Int. Math. Res. Notices , vol.10 , pp. 505-520
    • Topping, P.1
  • 26
    • 0013200078 scopus 로고    scopus 로고
    • Flow alignment in nematic liquid crystals in flows with cylindrical symmetry
    • Van der Hout, R.: Flow alignment in nematic liquid crystals in flows with cylindrical symmetry. Differ. Integral Equal. 14(2), 189-211 (2001)
    • (2001) Differ. Integral Equal. , vol.14 , Issue.2 , pp. 189-211
    • Van Der Hout, R.1
  • 27
    • 84963483284 scopus 로고
    • Travelling wavefronts of reaction-diffusion equations in cylindrical domains
    • Vega, J.M.: Travelling wavefronts of reaction-diffusion equations in cylindrical domains. Comm. Partial Differ. Equat. 18, 505-531 (1993)
    • (1993) Comm. Partial Differ. Equat. , vol.18 , pp. 505-531
    • Vega, J.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.