메뉴 건너뛰기




Volumn 11, Issue 5, 2000, Pages 491-514

The dynamics of boundary spikes for a nonlocal reaction-diffusion model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034365035     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792500004253     Document Type: Article
Times cited : (11)

References (24)
  • 2
    • 84968466504 scopus 로고
    • Collocation software for boundary value ODEs
    • ASCHER, U., CHRISTIANSEN, R. & RUSSELL, R. (1979) Collocation software for boundary value ODEs. Math. Comp. 33, 659-679.
    • (1979) Math. Comp. , vol.33 , pp. 659-679
    • Ascher, U.1    Christiansen, R.2    Russell, R.3
  • 5
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • GIERER, A. & MEINHARDT, H. (1972) A theory of biological pattern formation. Kybernetik, 12, 30-39.
    • (1972) Kybernetik , vol.12 , pp. 30-39
    • Gierer, A.1    Meinhardt, H.2
  • 6
    • 0000860177 scopus 로고    scopus 로고
    • Multi-peaked solutions to a semilinear Neumann problem
    • GUI, C. (1996) Multi-peaked solutions to a semilinear Neumann problem. Duke Math. J. 84(3), 739-769.
    • (1996) Duke Math. J. , vol.84 , Issue.3 , pp. 739-769
    • Gui, C.1
  • 7
    • 0002610597 scopus 로고    scopus 로고
    • Multiple interior peak solutions for some singularly perturbed Neumann problems
    • GUI, C. & WEI, J. (1999) Multiple interior peak solutions for some singularly perturbed Neumann problems. J. Diff. Eq. 158(1), 1-27.
    • (1999) J. Diff. Eq. , vol.158 , Issue.1 , pp. 1-27
    • Gui, C.1    Wei, J.2
  • 8
    • 0001067122 scopus 로고
    • Order and Localization in Reaction-Diffusion Pattern
    • HARRISON, L. & HOLLOWAY, D. (1995) Order and Localization in Reaction-Diffusion Pattern. Physica A, 222, 210-233.
    • (1995) Physica A , vol.222 , pp. 210-233
    • Harrison, L.1    Holloway, D.2
  • 10
    • 0033723712 scopus 로고    scopus 로고
    • A metastable spike solution for a nonLocal reaction-diffusion model
    • IRON, D. & WARD, M. J. (2000) A metastable spike solution for a nonLocal reaction-diffusion model. SIAM J. Appl. Math. 60(3), 778-802.
    • (2000) SIAM J. Appl. Math. , vol.60 , Issue.3 , pp. 778-802
    • Iron, D.1    Ward, M.J.2
  • 11
    • 0023399088 scopus 로고
    • A variational approach to nonlinear singularly perturbed boundary value problems
    • KATH, W., KNESSL, C. & MATKOWSKY, B. (1987) A variational approach to nonlinear singularly perturbed boundary value problems. Studies in Appl. Math. 77, 61-88.
    • (1987) Studies in Appl. Math. , vol.77 , pp. 61-88
    • Kath, W.1    Knessl, C.2    Matkowsky, B.3
  • 12
    • 0002873885 scopus 로고    scopus 로고
    • Exponentially slow dynamics and interfaces intersecting the boundary
    • KOWALCZYK, M. (1997) Exponentially slow dynamics and interfaces intersecting the boundary. J. Diff. Eq. 138(1), 55-85.
    • (1997) J. Diff. Eq. , vol.138 , Issue.1 , pp. 55-85
    • Kowalczyk, M.1
  • 13
    • 0002057398 scopus 로고    scopus 로고
    • Multiple spike layers in the shadow Gierer-Meinhardt system: Existence of equilibria and approximate invariant manifold
    • KOWALCZYK, M. (1999) Multiple spike layers in the shadow Gierer-Meinhardt system: Existence of equilibria and approximate invariant manifold. Duke Math J. 98(1) 59-111.
    • (1999) Duke Math J. , vol.98 , Issue.1 , pp. 59-111
    • Kowalczyk, M.1
  • 14
    • 0000214161 scopus 로고
    • On the diffusion coefficient of a semilinear Neumann problem
    • Calculus of Variations and Partial Differential Equations, Trento, Italy. Springer-Verlag, Berlin
    • LIN, C. & NI, W. (1988) On the diffusion coefficient of a semilinear Neumann problem. Calculus of Variations and Partial Differential Equations, Trento, Italy. Lecture Notes in Mathemtics, 1340, Springer-Verlag, Berlin, pp. 160-174.
    • (1988) Lecture Notes in Mathemtics , vol.1340 , pp. 160-174
    • Lin, C.1    Ni, W.2
  • 15
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion, and their spike-layer steady-states
    • NI, W. (1998) Diffusion, cross-diffusion, and their spike-layer steady-states. Notices of the AMS, 45(1), 9-18.
    • (1998) Notices of the AMS , vol.45 , Issue.1 , pp. 9-18
    • Ni, W.1
  • 16
    • 84990581933 scopus 로고
    • On the shape of least-energy solutions to a semilinear Neumann problem
    • NI, W. & TAKAGI, I. (1991) On the shape of least-energy solutions to a semilinear Neumann problem. Comm. Pure Appl. Math. XLIV, 819-851.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 819-851
    • Ni, W.1    Takagi, I.2
  • 17
    • 0000999835 scopus 로고
    • An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt
    • SAROCKA, D. & BERNOFF, A. (1995) An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt. Physica D, 85, 348-374.
    • (1995) Physica D , vol.85 , pp. 348-374
    • Sarocka, D.1    Bernoff, A.2
  • 19
    • 0002081432 scopus 로고    scopus 로고
    • The dynamics of drops and attached interfaces for the constrained Allen-Cahn equation
    • submitted
    • STAFFORD, D., WARD, M. J. & WETTON, B. (2000) The dynamics of drops and attached interfaces for the constrained Allen-Cahn equation. Euro. J. Appl. Math. (submitted).
    • (2000) Euro. J. Appl. Math.
    • Stafford, D.1    Ward, M.J.2    Wetton, B.3
  • 20
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • TURING, A. (1952) The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. B, 327, 37-72.
    • (1952) Phil. Trans. Roy. Soc. B , vol.327 , pp. 37-72
    • Turing, A.1
  • 21
    • 0042624339 scopus 로고    scopus 로고
    • An asymptotic analysis of localized solutions for some reaction-diffusion models in multi-dimensional domains
    • WARD, M. (1996) An asymptotic analysis of localized solutions for some reaction-diffusion models in multi-dimensional domains. Stud. Appl. Math. 97(2), 103-126.
    • (1996) Stud. Appl. Math. , vol.97 , Issue.2 , pp. 103-126
    • Ward, M.1
  • 23
    • 0033414750 scopus 로고    scopus 로고
    • On single interior spike solutions for the Gierer-Meinhardt system: Uniqueness and stability estimates
    • WEI, J. (1999) On single interior spike solutions for the Gierer-Meinhardt system: Uniqueness and stability estimates. Euro. J. Appl. Math. 10(4), 353-378.
    • (1999) Euro. J. Appl. Math. , vol.10 , Issue.4 , pp. 353-378
    • Wei, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.