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Volumn 131, Issue 4, 2001, Pages 1457-1480

Uniqueness and critical spectrum of boundary spike solutions

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EID: 33747020872     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500001487     Document Type: Article
Times cited : (28)

References (30)
  • 1
    • 0000582570 scopus 로고
    • The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions
    • N. Alikakos and G. Fusco. The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions. Indiana Univ. Math. J. 42 (1993), 637-674.
    • (1993) Indiana Univ. Math. J. , vol.42 , pp. 637-674
    • Alikakos, N.1    Fusco, G.2
  • 2
    • 84963254790 scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. I. Spectral estimates
    • N. Alikakos and G. Fusco. Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. I. Spectral estimates. Commun. PDEs 19 (1994), 1397-1447.
    • (1994) Commun. PDEs , vol.19 , pp. 1397-1447
    • Alikakos, N.1    Fusco, G.2
  • 3
    • 0032397594 scopus 로고    scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
    • N. Alikakos and G. Fusco. Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: the motion of bubbles. Arch. Ration. Mech. Analysis 141 (1998), 1-61.
    • (1998) Arch. Ration. Mech. Analysis , vol.141 , pp. 1-61
    • Alikakos, N.1    Fusco, G.2
  • 5
    • 0030594276 scopus 로고    scopus 로고
    • Critical spectrum and stability of interfaces for a class of reaction-diffusion equations
    • N. Alikakos, G. Fusco and V. Stefanopoulas. Critical spectrum and stability of interfaces for a class of reaction-diffusion equations. J. Diff. Eqns 126 (1996), 106-167.
    • (1996) J. Diff. Eqns , vol.126 , pp. 106-167
    • Alikakos, N.1    Fusco, G.2    Stefanopoulas, V.3
  • 6
    • 0041740942 scopus 로고    scopus 로고
    • Mullins-Sekerka motion of small droplets on a fixed boundary
    • N. Alikakos, P. Bates, X. Chen and G. Fusco. Mullins-Sekerka motion of small droplets on a fixed boundary. J. Geom. Analysis 10 (2000), 575-596.
    • (2000) J. Geom. Analysis , vol.10 , pp. 575-596
    • Alikakos, N.1    Bates, P.2    Chen, X.3    Fusco, G.4
  • 7
    • 0027647619 scopus 로고
    • The dynamics of nucleation for the Cahn-Hilliard equation
    • P. Bates and P. Fife. The dynamics of nucleation for the Cahn-Hilliard equation. SIAM J. Appl. Math. 53 (1993), 990-1008.
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 990-1008
    • Bates, P.1    Fife, P.2
  • 8
    • 84894599571 scopus 로고    scopus 로고
    • Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability
    • P. Bates, E. N. Dancer and J. Shi. Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. Adv. Diff. Eqns 4 (1999), 1-69.
    • (1999) Adv. Diff. Eqns , vol.4 , pp. 1-69
    • Bates, P.1    Dancer, E.N.2    Shi, J.3
  • 9
    • 0033233496 scopus 로고    scopus 로고
    • On the role of mean curvature in some singularly perturbed Neumann problems
    • M. del Pino, P. Felmer and J. Wei. On the role of mean curvature in some singularly perturbed Neumann problems. SIAM J. Math. Analysis 31 (1999), 63-79.
    • (1999) SIAM J. Math. Analysis , vol.31 , pp. 63-79
    • Del Pino, M.1    Felmer, P.2    Wei, J.3
  • 11
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • A. Gierer and H. Meinhardt. A theory of biological pattern formation. Kybernetik 12 (1972), 30-39.
    • (1972) Kybernetik , vol.12 , pp. 30-39
    • Gierer, A.1    Meinhardt, H.2
  • 12
    • 0000860177 scopus 로고    scopus 로고
    • Multi-peak solutions for a semilinear Neumann problem
    • C. Gui. Multi-peak solutions for a semilinear Neumann problem. Duke Math. J. 84 (1996), 739-769.
    • (1996) Duke Math. J. , vol.84 , pp. 739-769
    • Gui, C.1
  • 13
    • 0002610597 scopus 로고    scopus 로고
    • Multiple interior peak solutions for some singular perturbation problems
    • C. Gui and J. Wei. Multiple interior peak solutions for some singular perturbation problems. J. Diff. Eqns 158 (1999), 1-27.
    • (1999) J. Diff. Eqns , vol.158 , pp. 1-27
    • Gui, C.1    Wei, J.2
  • 14
    • 0002025752 scopus 로고    scopus 로고
    • Multiple boundary peak solutions for some singularly perturbed Neumann problems
    • C. Gui, J. Wei and M. Winter. Multiple boundary peak solutions for some singularly perturbed Neumann problems. Annls Henri Poincaré 17 (2000), 47-82.
    • (2000) Annls Henri Poincaré , vol.17 , pp. 47-82
    • Gui, C.1    Wei, J.2    Winter, M.3
  • 15
    • 84958370767 scopus 로고
    • Multiple wells in the semi-classical limit. I
    • B. Helfler and J. Sjöstrand. Multiple wells in the semi-classical limit. I. Commun. PDEs 9 (1984), 337-408.
    • (1984) Commun. PDEs , vol.9 , pp. 337-408
    • Helfler, B.1    Sjöstrand, J.2
  • 16
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • K. F. Keller and L. A. Segel. Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26 (1970), 399-415.
    • (1970) J. Theor. Biol. , vol.26 , pp. 399-415
    • Keller, K.F.1    Segel, L.A.2
  • 18
    • 0000984635 scopus 로고    scopus 로고
    • On a singularly perturbed equation with Neumann boundary condition
    • Y.-Y. Li. On a singularly perturbed equation with Neumann boundary condition. Commun. PDEs 23 (1998), 487-545.
    • (1998) Commun. PDEs , vol.23 , pp. 487-545
    • Li, Y.-Y.1
  • 19
    • 0000214161 scopus 로고
    • On the diffusion coefficient of a semilinear Neumann problem
    • Calculus of variations and partial differential equations. Springer
    • C.-S. Lin and W.-M. Ni. On the diffusion coefficient of a semilinear Neumann problem. In Calculus of variations and partial differential equations. Lecture Notes in Mathematics, vol. 1340, pp. 160-174 (Springer, 1988).
    • (1988) Lecture Notes in Mathematics , vol.1340 , pp. 160-174
    • Lin, C.-S.1    Ni, W.-M.2
  • 20
    • 0002542873 scopus 로고
    • Large amplitude stationary solutions to a chemotaxis systems
    • C.-S. Lin, W.-M. Ni and I. Takagi. Large amplitude stationary solutions to a chemotaxis systems. J. Diff. Eqns 72 (1988), 1-27.
    • (1988) J. Diff. Eqns , vol.72 , pp. 1-27
    • Lin, C.-S.1    Ni, W.-M.2    Takagi, I.3
  • 21
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion, and their spike-layer steady states
    • W.-M. Ni. Diffusion, cross-diffusion, and their spike-layer steady states. Not. Am. Math. Soc. 45 (1998), 9-18.
    • (1998) Not. Am. Math. Soc. , vol.45 , pp. 9-18
    • Ni, W.-M.1
  • 22
    • 84990581933 scopus 로고
    • On the shape of least energy solution to a semilinear Neumann problem
    • W.-M. Ni and I. Takagi. On the shape of least energy solution to a semilinear Neumann problem. Commun. Pure Appl. Math. 41 (1991), 819-851.
    • (1991) Commun. Pure Appl. Math. , vol.41 , pp. 819-851
    • Ni, W.-M.1    Takagi, I.2
  • 23
    • 84971179248 scopus 로고
    • Locating the peaks of least energy solutions to a semilinear Neumann problem
    • W.-M. Ni and I. Takagi. Locating the peaks of least energy solutions to a semilinear Neumann problem. Duke Math. J. 70 (1993), 247-281.
    • (1993) Duke Math. J. , vol.70 , pp. 247-281
    • Ni, W.-M.1    Takagi, I.2
  • 24
    • 0001672333 scopus 로고
    • Point-condensation generated by a reaction-diffusion system in axially symmetric domains
    • W.-M. Ni and I. Takagi. Point-condensation generated by a reaction-diffusion system in axially symmetric domains. Jpn J. Ind. Appl. Math. 12 (1995), 327-365.
    • (1995) Jpn J. Ind. Appl. Math. , vol.12 , pp. 327-365
    • Ni, W.-M.1    Takagi, I.2
  • 25
    • 0031562011 scopus 로고    scopus 로고
    • On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem
    • J. Wei. On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem. J. Diff. Eqns 134 (1997), 104-133.
    • (1997) J. Diff. Eqns , vol.134 , pp. 104-133
    • Wei, J.1
  • 26
    • 0347188202 scopus 로고    scopus 로고
    • On the interior spike layer solutions for some singular perturbation problems
    • J. Wei. On the interior spike layer solutions for some singular perturbation problems. Proc. R. Soc. Edinb. A 128 (1998), 849-874.
    • (1998) Proc. R. Soc. Edinb. A , vol.128 , pp. 849-874
    • Wei, J.1
  • 27
    • 0032398054 scopus 로고    scopus 로고
    • On the interior spike layer solutions of singularly perturbed semilinear Neumann problem
    • J. Wei. On the interior spike layer solutions of singularly perturbed semilinear Neumann problem. Tohoku Math. J. 50 (1998), 159-178.
    • (1998) Tohoku Math. J. , vol.50 , pp. 159-178
    • Wei, J.1
  • 28
    • 0033414750 scopus 로고    scopus 로고
    • On single interior spike solutions of Gierer-Meinhardt system: Uniqueness and spectrum estimates
    • J. Wei. On single interior spike solutions of Gierer-Meinhardt system: uniqueness and spectrum estimates. Eur. J. Appl. Math. 10 (1999), 353-378.
    • (1999) Eur. J. Appl. Math. , vol.10 , pp. 353-378
    • Wei, J.1
  • 29
    • 0000585101 scopus 로고    scopus 로고
    • Stationary solutions for the Cahn-Hilliard equation
    • J. Wei and M. Winter. Stationary solutions for the Cahn-Hilliard equation. Annls Henri Poincaré 15 (1998), 459-492.
    • (1998) Annls Henri Poincaré , vol.15 , pp. 459-492
    • Wei, J.1    Winter, M.2
  • 30
    • 0000068099 scopus 로고    scopus 로고
    • Multiple boundary spike solutions for a wide class of singular perturbation problems
    • J. Wei and M. Winter. Multiple boundary spike solutions for a wide class of singular perturbation problems. J. Lond. Math. Soc. 59 (1999), 585-606.
    • (1999) J. Lond. Math. Soc. , vol.59 , pp. 585-606
    • Wei, J.1    Winter, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.