메뉴 건너뛰기




Volumn 98, Issue 1, 1999, Pages 59-111

Multiple spike layers in the shadow gierermeinhardt system: Existence of equilibria and the quasi-invariant manifold

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0002057398     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-09802-2     Document Type: Article
Times cited : (45)

References (42)
  • 1
    • 0003308723 scopus 로고
    • Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigen functions of N-Body Schrodinger Operators
    • Princeton Univ. Press, Princeton, N.J
    • S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigen functions of N-Body Schrodinger Operators, Math. Notes 29, Princeton Univ. Press, Princeton, N.J., 1982.
    • (1982) Math. Notes , vol.29
    • Agmon, S.1
  • 3
    • 44949275928 scopus 로고
    • Slow motion for the Cahn-Hilliard equation in one space dimension
    • N. D. Alikakos, P. W. Bates, and G. Fusco, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Differential Equations 90 (1991), 81-135.
    • (1991) J. Differential Equations , vol.90 , pp. 81-135
    • Alikakos, N.D.1    Bates, P.W.2    Fusco, G.3
  • 4
    • 84963254790 scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions, I: Spectral estimates
    • N. D. Alikakos and G. Fusco, Slow dynamics for the Cahn-Hilliard equation in higher space dimensions, I: Spectral estimates, Comm. Partial Differential Equations 19 (1994), 1397-1447.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1397-1447
    • Alikakos, N.D.1    Fusco, G.2
  • 5
    • 0032397594 scopus 로고    scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions, II: The motion of bubbles
    • N. D. Alikakos and G. Fusco, Slow dynamics for the Cahn-Hilliard equation in higher space dimensions, II: The motion of bubbles, Arch. Rational Mech. Anal. 141 (1998), 1-61.
    • (1998) Arch. Rational Mech. Anal , vol.141 , pp. 1-61
    • Alikakos, N.D.1    Fusco, G.2
  • 6
    • 0000407342 scopus 로고    scopus 로고
    • Finite-dimensional dynamics and interfaces intersecting the boundary
    • N. D. Alikakos, G. Fusco, and M. Kowalczyk, Finite-dimensional dynamics and interfaces intersecting the boundary, Indiana Univ. Math. J. 45 (1996), 1119-1155.
    • (1996) Indiana Univ. Math. J , vol.45 , pp. 1119-1155
    • Alikakos, N.D.1    Fusco, G.2    Kowalczyk, M.3
  • 7
    • 85037889322 scopus 로고    scopus 로고
    • Critical points of a singular perturbation problem via reduced energy and local linking
    • N. D. Alikakos and M. Kowalczyk, Critical points of a singular perturbation problem via reduced energy and local linking, submitted.
    • Submitted
    • Alikakos, N.D.1    Kowalczyk, M.2
  • 8
    • 85037898606 scopus 로고    scopus 로고
    • Multiple-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability
    • P. W. Bates, E. N. Dancer, and J. Shi, Multiple-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability, preprint.
    • Preprint
    • Bates, P.W.1    Dancer, E.N.2    Shi, J.3
  • 9
    • 0027647619 scopus 로고
    • The dynamics of nucleation for the Cahn-Hilliard equation, SIAM
    • P. W. Bates and P. Fife, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math. 53 (1993), 990-1008.
    • (1993) J. Appl. Math , vol.53 , pp. 990-1008
    • Bates, P.W.1    Fife, P.2
  • 10
    • 84894543756 scopus 로고
    • Nucleating solutions for the Cahn-Hilliard equation in higher space dimension, lecture given at the SIAM Conference on Applications of Dynamical Systems, Snowbird
    • October
    • P. W. Bates and G. Fusco, Nucleating solutions for the Cahn-Hilliard equation in higher space dimension, lecture given at the SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, 15-19 October 1992.
    • (1992) Utah , pp. 15-19
    • Bates, P.W.1    Fusco, G.2
  • 11
    • 85037887747 scopus 로고    scopus 로고
    • Equilibria with many nuclei for the Cahn-Hilliard equation
    • P. W. Bates and G. Fusco, Equilibria with many nuclei for the Cahn-Hilliard equation, preprint.
    • Preprint
    • Bates, P.W.1    Fusco, G.2
  • 12
    • 0002556198 scopus 로고
    • The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
    • V. Benci and G. Cerami, The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems, Arch. Rational Mech. Anal. 114 (1991), 79-93.
    • (1991) Arch. Rational Mech. Anal , vol.114 , pp. 79-93
    • Benci, V.1    Cerami, G.2
  • 13
    • 0001067029 scopus 로고    scopus 로고
    • On the existence and profile of multi peaked solutions to singularly perturbed semilinear Dirichlet problem, Discrete Contin
    • D. Cao, E. N. Dancer, E. S. Noussair, and S. Yan, On the existence and profile of multi peaked solutions to singularly perturbed semilinear Dirichlet problem, Discrete Contin. Dynam. Systems 2 (1996), 221-236.
    • (1996) Dynam. Systems , vol.2 , pp. 221-236
    • Cao, D.1    Dancer, E.N.2    Noussair, E.S.3    Yan, S.4
  • 16
    • 85037923382 scopus 로고    scopus 로고
    • Multi-peak solutions for some singular perturbation problems
    • M. del Pino, P. L. Felmer, and J. Wei, Multi-peak solutions for some singular perturbation problems, preprint.
    • Preprint
    • Del Pino, M.1    Felmer, P.L.2    Wei, J.3
  • 17
    • 77956949687 scopus 로고
    • Partial Differential Equations of Parabolic Type
    • Englewood Cliffs, N.J
    • A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
    • (1964) Prentice-Hall
    • Friedman, A.1
  • 18
    • 0001863910 scopus 로고
    • Slow motion manifolds, dormant instability and singular perturbation
    • G. Fusco and J. Hale, Slow motion manifolds, dormant instability and singular perturbation, J. Dynam. Differential Equations 1 (1989), 75-94.
    • (1989) J. Dynam. Differential Equations , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J.2
  • 19
    • 0000924617 scopus 로고
    • Symmetry of positive solutions of nonlinear elliptic equations in Rn
    • Mathematical Analysis and Applications, Part A, Suppl. Stud. 7A, Academic Press, New York
    • n” Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Stud. 7A, Academic Press, New York, 1981, 369-402.
    • (1981) Adv. Math. , pp. 369-402
    • Gidas, B.1    Ni, W.-M.2    Nirenberg, L.3
  • 20
    • 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
  • 21
    • 0000860177 scopus 로고    scopus 로고
    • Multipeaked solutions to a semilinear Neumann problem
    • C. Gui, Multipeaked solutions to a semilinear Neumann problem, Duke Math. J. 84 (1996), 739-769.
    • (1996) Duke Math. J , vol.84 , pp. 739-769
    • Gui, C.1
  • 22
    • 0002298523 scopus 로고    scopus 로고
    • Diffusive coupling, dissipation and synchronization
    • J. Hale and H. Sakamoto, Diffusive coupling, dissipation and synchronization, J. Dynam. Differential Equations 9 (1997), 1-52.
    • (1997) J. Dynam. Differential Equations , vol.9 , pp. 1-52
    • Hale, J.1    Sakamoto, H.2
  • 23
    • 0003904047 scopus 로고
    • Reaction-diffusion theory of localized structures with application to vertebrate organogenesis
    • University of British Columbia, Vancouver, March
    • D. M. Holloway, Reaction-diffusion theory of localized structures with application to vertebrate organogenesis, Ph.D. thesis, University of British Columbia, Vancouver, March 1995.
    • (1995) Ph.D. Thesis
    • Holloway, D.M.1
  • 24
    • 0018003001 scopus 로고
    • Activators and inhibitors in pattern formation
    • J. P. Keener, Activators and inhibitors in pattern formation, Stud. Appl. Math 59 (1978), 1-23.
    • (1978) Stud. Appl. Math , vol.59 , pp. 1-23
    • Keener, J.P.1
  • 25
    • 85037903063 scopus 로고    scopus 로고
    • The reduced energy, minimax principle and singular perturbation problems
    • M. Kowalczyk, The reduced energy, minimax principle and singular perturbation problems, forthcoming.
    • Forthcoming
    • Kowalczyk, M.1
  • 26
    • 0040030535 scopus 로고    scopus 로고
    • Uniqueness of positive solutions of ku +f(U) = 0 inanannulus
    • M. K. Kwong and L. Zhang, Uniqueness of positive solutions of ku +f(u) = 0 inanannulus, J. Differential Equations 138 (1997), 55-85.
    • (1997) J. Differential Equations , vol.138 , pp. 55-85
    • Kwong, M.K.1    Zhang, L.2
  • 27
    • 0001191547 scopus 로고
    • Morse theory and multiple positive solutions to a Neumann problem
    • M. Lazzo, Morse theory and multiple positive solutions to a Neumann problem, Ann. Mat.Pura Appl. (4) 168 (1995), 205-217.
    • (1995) Ann. Mat.Pura Appl. , vol.4 , Issue.168 , pp. 205-217
    • Lazzo, M.1
  • 28
    • 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. Differential Equations 72 (1988), 1-27.
    • (1988) J. Differential Equations , vol.72 , pp. 1-27
    • Lin, C.-S.1    Ni, W.-M.2    Takagi, I.3
  • 29
    • 34247366525 scopus 로고
    • Quelques méthodes de résolution des problémes aux limites non linéaires
    • Paris
    • J.-L. Lions, Quelques méthodes de résolution des problémes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969.
    • (1969) Dunod, Gauthier-Villars
    • Lions, J.-L.1
  • 31
    • 84990581933 scopus 로고
    • On the shape of least-energy solutions to a semilinear Neumann problem
    • W.-M. Ni and I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991), 819-851.
    • (1991) Comm. Pure Appl. Math , vol.44 , pp. 819-851
    • Ni, W.-M.1    Takagi, I.2
  • 32
    • 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
  • 33
    • 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, Japan J. Indust. Appl. Math. 12 (1995), 327-365.
    • (1995) Japan J. Indust. Appl. Math , vol.12 , pp. 327-365
    • Ni, W.-M.1    Takagi, I.2
  • 34
    • 85037878557 scopus 로고    scopus 로고
    • Stability analysis of point condensation solutions
    • W.-M. Ni, I. Takagi, and E. Yanagida, Stability analysis of point condensation solutions, preprint.
    • Preprint
    • Ni, W.-M.1    Takagi, I.2    Yanagida, E.3
  • 35
    • 84990662413 scopus 로고
    • On the location and profile of spike layer solutions to singularly perturbed semilinear Dirichletproblem
    • W.-M. Ni and J. Wei, On the location and profile of spike layer solutions to singularly perturbed semilinear Dirichletproblem, Comm. Pure Appl. Math. 48 (1995), 731-768.
    • (1995) Comm. Pure Appl. Math , vol.48 , pp. 731-768
    • Ni, W.-M.1    Wei, J.2
  • 36
    • 0001347301 scopus 로고
    • Global structure of bifurcating solutions of some reaction-diffusion systems
    • SIAM
    • Y. Nishiura, Global structure of bifurcating solutions of some reaction-diffusion systems, SIAM J. Math. Anal. 13 (1982), 555-593.
    • (1982) J. Math. Anal , vol.13 , pp. 555-593
    • Nishiura, Y.1
  • 37
    • 0000864203 scopus 로고
    • Point-condensation for a reaction-diffusion system
    • I. Takagi, Point-condensation for a reaction-diffusion system, J. Differential Equations 61 (1986), 208-249.
    • (1986) J. Differential Equations , vol.61 , pp. 208-249
    • Takagi, I.1
  • 38
    • 21144478287 scopus 로고
    • On the existence of multiple, single-peaked solutions for a semilinear Neumann problem
    • Z. Q. Wang, On the existence of multiple, single-peaked solutions for a semilinear Neumann problem, Arch. Rational Mech. Anal. 120 (1992), 375-399.
    • (1992) Arch. Rational Mech. Anal , vol.120 , pp. 375-399
    • Wang, Z.Q.1
  • 39
    • 0042624339 scopus 로고    scopus 로고
    • An asymptotic analysis of localized solutions for some reaction-diffusion models in multidimensional domains
    • M. Ward, An asymptotic analysis of localized solutions for some reaction-diffusion models in multidimensional domains, Stud. Appl. Math. 97 (1996), 103-126.
    • (1996) Stud. Appl. Math , vol.97 , pp. 103-126
    • Ward, M.1
  • 41
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem
    • J. Wei, On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996), 315-333.
    • (1996) J. Differential Equations , vol.129 , pp. 315-333
    • Wei, J.1
  • 42
    • 0032398054 scopus 로고    scopus 로고
    • On the interior spike layer solutions to a singularly perturbed Neumann problem
    • J. Wei, On the interior spike layer solutions to a singularly perturbed Neumann problem, Tôhoku Math. J. (2) 50 (1998), 159-178.
    • (1998) Tôhoku Math. J. , vol.2 , Issue.50 , pp. 159-178
    • Wei, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.