메뉴 건너뛰기




Volumn 14, Issue 5, 2003, Pages 513-545

Reduced wave Green's Functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0242626885     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792503005254     Document Type: Article
Times cited : (29)

References (33)
  • 2
    • 0034687912 scopus 로고    scopus 로고
    • Equilibria with many nuclei for the Cahn-Hilliard equation
    • BATES, P. & Fusco, N. (2000) Equilibria with many nuclei for the Cahn-Hilliard equation. J. Diff. Eq. 160(2), 283-356.
    • (2000) J. Diff. Eq. , vol.160 , Issue.2 , pp. 283-356
    • Bates, P.1    Fusco, N.2
  • 3
    • 0010365974 scopus 로고    scopus 로고
    • Large amplitude solutions of spatially non-homogeneous non-local reaction-diffusion equations
    • BOSE, A. & KRIEOSMANN, G. (2000) Large amplitude solutions of spatially non-homogeneous non-local reaction-diffusion equations. Meth. & Appl., Anal. 7(2), 295-312.
    • (2000) Meth. & Appl., Anal. , vol.7 , Issue.2 , pp. 295-312
    • Bose, A.1    Krieosmann, G.2
  • 4
    • 0033297031 scopus 로고    scopus 로고
    • The finite element approximation of seminlinear elliptic partial differential equations with critical exponents in the cube
    • BUUD, C. J., HUMPHRIES, A. B. & WATHEN, A. J. (1999) The finite element approximation of seminlinear elliptic partial differential equations with critical exponents in the cube. SIAM J. Sci. Comput. 20(5), 1875-1904.
    • (1999) SIAM J. Sci. Comput. , vol.20 , Issue.5 , pp. 1875-1904
    • Buud, C.J.1    Humphries, A.B.2    Wathen, A.J.3
  • 5
    • 84972581369 scopus 로고
    • Convexity of solutions of semilinear elliptic equations
    • CAFFARELLI, L. A. & FRIEDMAN, A. (1985) Convexity of solutions of semilinear elliptic equations. Duke Math. J. 52(2), 431-456.
    • (1985) Duke Math. J. , vol.52 , Issue.2 , pp. 431-456
    • Caffarelli, L.A.1    Friedman, A.2
  • 6
    • 11744295460 scopus 로고    scopus 로고
    • Design and application of a gradient-weighted moving finite element code I: In two dimensions
    • CARLSON, N. N. & MILLER, K. (1998) Design and application of a gradient-weighted moving finite element code I: in two dimensions. SIAM J. Sci. Comput. 19(3), 728-765.
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.3 , pp. 728-765
    • Carlson, N.N.1    Miller, K.2
  • 7
    • 0001070724 scopus 로고    scopus 로고
    • Design and application of a gradient-weighted moving finite element code II: In two dimensions
    • CARLSON, N. N. & MILLER, K. (1998) Design and application of a gradient-weighted moving finite element code II: in two dimensions. SIAM J. Sci. Comput. 19(3), 766-798.
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.3 , pp. 766-798
    • Carlson, N.N.1    Miller, K.2
  • 8
    • 0242631771 scopus 로고    scopus 로고
    • Private communication
    • CARLSON, N. N. Private communication.
    • Carlson, N.N.1
  • 9
    • 0001265467 scopus 로고    scopus 로고
    • Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system
    • CHEN, X. & KOWALCZYK, M. (2001) Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system. Adv. Diff. Equal. 6(7), 847-872.
    • (2001) Adv. Diff. Equal. , vol.6 , Issue.7 , pp. 847-872
    • Chen, X.1    Kowalczyk, M.2
  • 10
    • 0035527617 scopus 로고    scopus 로고
    • Dynamics of an interior spike in the Gierer-Meinhardt system
    • CHEN, X. & KOWALCYZK, M. (2001) Dynamics of an interior spike in the Gierer-Meinhardt system. SIAM. J. Math. Anal. 33(1), 172-193.
    • (2001) SIAM. J. Math. Anal. , vol.33 , Issue.1 , pp. 172-193
    • Chen, X.1    Kowalcyzk, M.2
  • 11
    • 0000706319 scopus 로고    scopus 로고
    • Pattern formation in the one-dimensional Gray-Scott model
    • DOELMAN, A., KAPER, T. J. & ZEGELING, P. (1997) Pattern formation in the one-dimensional Gray-Scott model. Nonlinearity, 10(2), 523-563.
    • (1997) Nonlinearity , vol.10 , Issue.2 , pp. 523-563
    • Doelman, A.1    Kaper, T.J.2    Zegeling, P.3
  • 12
    • 0242716046 scopus 로고    scopus 로고
    • Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt system in two spatial dimensions
    • EI, S. I. & WEI, J. (2002) Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt system in two spatial dimensions. Japan J. Ind. Appl. Math. 19(2), 181-226.
    • (2002) Japan J. Ind. Appl. Math. , vol.19 , Issue.2 , pp. 181-226
    • Ei, S.I.1    Wei, J.2
  • 13
    • 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
  • 14
    • 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
  • 15
    • 84974002359 scopus 로고
    • On the convexity of a solution of Liouville's equation
    • GUSTAFSSON, B. (1990) On the convexity of a solution of Liouville's equation. Duke Math. J. 60(2), 303-311.
    • (1990) Duke Math. J. , vol.60 , Issue.2 , pp. 303-311
    • Gustafsson, B.1
  • 16
    • 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
  • 17
    • 0033723712 scopus 로고    scopus 로고
    • A metastable spike solution for a non-local reaction-diffusion model
    • IRON, D. & WARD, M. J. (2000) A metastable spike solution for a non-local 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
  • 18
    • 0242463423 scopus 로고    scopus 로고
    • Vortex dynamics for the Ginzburg-Landau equation with Neumann condition
    • JIMBO, S. & MORITA, Y. (2001) Vortex dynamics for the Ginzburg-Landau equation with Neumann condition. Methods Appl. Anal. 8(3), 451-477.
    • (2001) Methods Appl. Anal. , vol.8 , Issue.3 , pp. 451-477
    • Jimbo, S.1    Morita, Y.2
  • 19
    • 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
  • 20
    • 0031512221 scopus 로고    scopus 로고
    • Ginzburg-Landau vortices: Dynamics, pinning and hysteresis
    • LIN, F. H. & DU, Q. (1997) Ginzburg-Landau vortices: dynamics, pinning and hysteresis. SIAM J. Math. Anal. 28(6), 1265-1293.
    • (1997) SIAM J. Math. Anal. , vol.28 , Issue.6 , pp. 1265-1293
    • Lin, F.H.1    Du, Q.2
  • 22
    • 84974747888 scopus 로고
    • Asymptotic analysis for two-dimensional elliptic Eigenvalue problems with exponentially dominated nonlinearities
    • NAGASAKI, K. & SUZUKI, T. (1990) Asymptotic analysis for two-dimensional elliptic Eigenvalue problems with exponentially dominated nonlinearities. Asymptotic Anal. 4, 173-188.
    • (1990) Asymptotic Anal. , vol.4 , pp. 173-188
    • Nagasaki, K.1    Suzuki, T.2
  • 24
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • TURING, A. (1952) The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. B, 237, 37-72.
    • (1952) Phil. Trans. Roy. Soc. B , vol.237 , pp. 37-72
    • Turing, A.1
  • 25
    • 0042624339 scopus 로고    scopus 로고
    • An asymptotic analysis of localized solutions for some reaction-diffusion models in multi-dimensional domains
    • WARD, M. J. (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.J.1
  • 26
    • 0027606742 scopus 로고
    • Summing logarithmic expansions for singularly perturbed Eigenvalue problems
    • WARD, M. J., HENSHAW, W. D. & KELLER, J. B. (1993) Summing logarithmic expansions for singularly perturbed Eigenvalue problems. SIAM J. Appl. Math. 53(3), 799-828.
    • (1993) SIAM J. Appl. Math. , vol.53 , Issue.3 , pp. 799-828
    • Ward, M.J.1    Henshaw, W.D.2    Keller, J.B.3
  • 27
    • 0036551784 scopus 로고    scopus 로고
    • The dynamics and pinning of a spike for a reaction-diffusion system
    • WARD, M. J., MCINERNEY, D., HOUSTON, P., GAVAGHAN, D. & MAINI, P. (2002) The dynamics and pinning of a spike for a reaction-diffusion system. SIAM J. Appl. Math. 62(4), 1297-1328.
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.4 , pp. 1297-1328
    • Ward, M.J.1    McInerney, D.2    Houston, P.3    Gavaghan, D.4    Maini, P.5
  • 28
    • 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. Europ. J. Appl. Math. 10(4), 353-378.
    • (1999) Europ. J. Appl. Math. , vol.10 , Issue.4 , pp. 353-378
    • Wei, J.1
  • 29
    • 0032398054 scopus 로고    scopus 로고
    • On the interior spike layer solutions to a singularly perturbed Neumann problem
    • WEI, J. (1998) On the interior spike layer solutions to a singularly perturbed Neumann problem. Tohoku Math. J. 50(2), 159-178.
    • (1998) Tohoku Math. J. , vol.50 , Issue.2 , pp. 159-178
    • Wei, J.1
  • 30
    • 0013236903 scopus 로고    scopus 로고
    • Spikes for the two-dimensional Gierer-Meinhardt system: The weak coupling case
    • WEI, J. & WINTER, M. (2001) Spikes for the two-dimensional Gierer-Meinhardt system: the weak coupling case. J. Nonlinear Sci. 11(6), 415-458.
    • (2001) J. Nonlinear Sci. , vol.11 , Issue.6 , pp. 415-458
    • Wei, J.1    Winter, M.2
  • 31
    • 0242546921 scopus 로고    scopus 로고
    • Spikes for the two-dimensional Gierer-Meinhardt system: The strong coupling case
    • WEI, J. & WINTER, M. (2002) Spikes for the two-dimensional Gierer-Meinhardt system: the strong coupling case. J. Diff. Eq. 178(2), 475-518.
    • (2002) J. Diff. Eq. , vol.178 , Issue.2 , pp. 475-518
    • Wei, J.1    Winter, M.2
  • 32
    • 0033249122 scopus 로고    scopus 로고
    • On the two-dimensional Gierer-Meinhardt system with strong coupling
    • WEI, J. & WINTER, M. (1999) On the two-dimensional Gierer-Meinhardt system with strong coupling. SIAM J. Math. Anal. 30(6), 1241-1263.
    • (1999) SIAM J. Math. Anal. , vol.30 , Issue.6 , pp. 1241-1263
    • Wei, J.1    Winter, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.