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Volumn 12, Issue 3, 1999, Pages 593-616

Existence, stability and metastability of point condensation patterns generated by the Gray-Scott system

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EID: 0033130430     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/3/011     Document Type: Article
Times cited : (35)

References (45)
  • 1
    • 0000437039 scopus 로고
    • The role of mean curvature in a semilinear Neumann problem involving the critical Sobolev exponent
    • Adimurthi, Mancinni G and Yadava S L 1995 The role of mean curvature in a semilinear Neumann problem involving the critical Sobolev exponent Comment. Part. Diff. Eqns 20 591-631
    • (1995) Comment. Part. Diff. Eqns , vol.20 , pp. 591-631
    • Adimurthi1    Mancinni, G.2    Yadava, S.L.3
  • 2
    • 43949176286 scopus 로고
    • Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity
    • Adimurthi, Pacella F and Yadava S L 1993 Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity J. Funct. Anal. 113 318-59
    • (1993) J. Funct. Anal. , vol.113 , pp. 318-359
    • Adimurthi1    Pacella, F.2    Yadava, S.L.3
  • 4
    • 0009151706 scopus 로고    scopus 로고
    • Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability
    • at press
    • Bates P, Dancer E N and Shi J Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability Adv. Diff. Eqns at press
    • Adv. Diff. Eqns
    • Bates, P.1    Dancer, E.N.2    Shi, J.3
  • 5
    • 0009221723 scopus 로고    scopus 로고
    • On the role of mean curvature in some singularly perturbed Neumann problems
    • to appear
    • del Pino M, Felmer P and Wei J On the role of mean curvature in some singularly perturbed Neumann problems Comment. Part. Diff. Eqns to appear
    • Comment. Part. Diff. Eqns
    • Del Pino, M.1    Felmer, P.2    Wei, J.3
  • 6
    • 0005468518 scopus 로고    scopus 로고
    • Stability of singular patterns in the ID Gray-Scott model: A matched asymptotic approach
    • Doelman A, Gardner A and Kaper T J 1998 Stability of singular patterns in the ID Gray-Scott model: A matched asymptotic approach Physica D 122 1-36
    • (1998) Physica D , vol.122 , pp. 1-36
    • Doelman, A.1    Gardner, A.2    Kaper, T.J.3
  • 7
    • 0001982150 scopus 로고    scopus 로고
    • A stability index analysis of 1D patterns of the Gray-Scott model
    • (Boston, MA: Boston University) submitted
    • Doelman A, Gardner A and Kaper T J A stability index analysis of 1D patterns of the Gray-Scott model Technical Report, Center for BioDynamics (Boston, MA: Boston University) submitted
    • Technical Report, Center for BioDynamics
    • Doelman, A.1    Gardner, A.2    Kaper, T.J.3
  • 8
    • 0000706319 scopus 로고    scopus 로고
    • Pattern formation in the one-dimensional Gray-Scott model
    • Doelman A, Kaper T and Zegeling P A 1997 Pattern formation in the one-dimensional Gray-Scott model Nonlinearity 10 523-63
    • (1997) Nonlinearity , vol.10 , pp. 523-563
    • Doelman, A.1    Kaper, T.2    Zegeling, P.A.3
  • 9
    • 0032194927 scopus 로고    scopus 로고
    • Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev expoenent
    • Gui C and Ghoussoub N 1998 Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev expoenent Math. Zeit. 229 443-74
    • (1998) Math. Zeit. , vol.229 , pp. 443-474
    • Gui, C.1    Ghoussoub, N.2
  • 10
    • 0009290368 scopus 로고    scopus 로고
    • New variational principles and multi-peak solutions for the semilinear Neumann problem involving the critical Sobolev exponent
    • Gui C and Ghoussoub N 1996 New variational principles and multi-peak solutions for the semilinear Neumann problem involving the critical Sobolev exponent Invited Papers, Canadian Mathematical Society
    • (1996) Invited Papers, Canadian Mathematical Society
    • Gui, C.1    Ghoussoub, N.2
  • 11
    • 0020607165 scopus 로고
    • Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability
    • Gray P and Scott S K 1983 Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability Chem. Engng Sci. 38 29-43
    • (1983) Chem. Engng Sci. , vol.38 , pp. 29-43
    • Gray, P.1    Scott, S.K.2
  • 12
    • 0021310291 scopus 로고
    • Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system
    • Gray P and Scott S K 1984 Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system A + 2B → 3B, B → C Chem. Engng Sci. 39 1087-97
    • (1984) A + 2B → 3B, B → C Chem. Engng Sci. , vol.39 , pp. 1087-1097
    • Gray, P.1    Scott, S.K.2
  • 13
    • 0000860177 scopus 로고    scopus 로고
    • Multi-peak solutions for a semilinear Neumann problem
    • Gui C 1996 Multi-peak solutions for a semilinear Neumann problem Duke Math. J. 84 739-69
    • (1996) Duke Math. J. , vol.84 , pp. 739-769
    • Gui, C.1
  • 17
    • 84972508309 scopus 로고
    • Uniqueness of positive solutions of Δu + f(u) = 0 in an annulus
    • Kwong M K and Zhang L 1991 Uniqueness of positive solutions of Δu + f(u) = 0 in an annulus Differ. Integ. Eqns 4 583-99
    • (1991) Differ. Integ. Eqns , vol.4 , pp. 583-599
    • Kwong, M.K.1    Zhang, L.2
  • 18
    • 0000984635 scopus 로고
    • On a singularly perturbed equation with Neumann boundary condition
    • Li Y-Y 1993 On a singularly perturbed equation with Neumann boundary condition Comment. Part. Diff. Eqns 23 487-545
    • (1993) Comment. Part. Diff. Eqns , vol.23 , pp. 487-545
    • Li, Y.-Y.1
  • 20
    • 0004034109 scopus 로고
    • New York: Springer
    • Lin C-S and Ni W-M 1986 On the diffusion coefficient of a semilinear Neumann problem Calculus of variations and partial differential equations (Trento, 1986) pp 160-174 Lin C-S and Ni W-M 1988 Lecture Notes in Math. (New York: Springer) p 1340
    • (1988) Lecture Notes in Math , pp. 1340
    • Lin, C.-S.1    Ni, W.-M.2
  • 22
    • 84973998562 scopus 로고
    • Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents
    • Ni W-M, Pan X and Takagi I 1992 Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents Duke Math. J. 67 1-20
    • (1992) Duke Math. J. , vol.67 , pp. 1-20
    • Ni, W.-M.1    Pan, X.2    Takagi, I.3
  • 23
    • 84990581933 scopus 로고
    • On the shape of least energy solution to a semilinear Neumann problem
    • Ni W-M and Takagi I 1991 On the shape of least energy solution to a semilinear Neumann problem Comm. Pure Appl. Math. 41 819-51
    • (1991) Comm. Pure Appl. Math. , vol.41 , pp. 819-851
    • Ni, W.-M.1    Takagi, I.2
  • 24
    • 84971179248 scopus 로고
    • Locating the peaks of least energy solutions to a semilinear Neumann problem
    • Ni W-M and Takagi I 1993 Locating the peaks of least energy solutions to a semilinear Neumann problem Duke Math. J. 70 247-81
    • (1993) Duke Math. J. , vol.70 , pp. 247-281
    • Ni, W.-M.1    Takagi, I.2
  • 25
    • 0001672333 scopus 로고
    • Point-condensation generated by a reaction-diffusion system in axially symmetric domains
    • Ni W-M and Takagi I 1995 Point-condensation generated by a reaction-diffusion system in axially symmetric domains Japan. J. Indust. Appl. Math. 12 327-65
    • (1995) Japan. J. Indust. Appl. Math. , vol.12 , pp. 327-365
    • Ni, W.-M.1    Takagi, I.2
  • 27
    • 4243718884 scopus 로고    scopus 로고
    • A skeleton structure of self-replicating dynamics
    • Preprint Laboratory of Nonlinear Studies, Hokkaido University at press
    • Nishiura Y and Ueyama D A skeleton structure of self-replicating dynamics Preprint Laboratory of Nonlinear Studies, Hokkaido University Physica D at press
    • Physica D
    • Nishiura, Y.1    Ueyama, D.2
  • 28
    • 84990662413 scopus 로고
    • On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlel problems
    • Ni W-M and Wei J 1995 On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlel problems Comment. Pure Appl. Math. 48 731-68
    • (1995) Comment. Pure Appl. Math. , vol.48 , pp. 731-768
    • Ni, W.-M.1    Wei, J.2
  • 29
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion, and their spike-layer steady states
    • Ni W-M 1998 Diffusion, cross-diffusion, and their spike-layer steady states Not. Am. Math. Soc. 45 9-18
    • (1998) Not. Am. Math. Soc. , vol.45 , pp. 9-18
    • Ni, W.-M.1
  • 30
    • 0001347301 scopus 로고
    • Global structure of bifurcation solutions of some reaction-diffusion systems
    • Nishiura Y 1982 Global structure of bifurcation solutions of some reaction-diffusion systems SIAM J. Math. Anal. 13 555-93
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 555-593
    • Nishiura, Y.1
  • 31
    • 0030101235 scopus 로고
    • Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
    • Petrov V, Scott S K and Showalter K 1994 Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system Phil. Trans. R. Soc. London A 347 631-42
    • (1994) Phil. Trans. R. Soc. London A , vol.347 , pp. 631-642
    • Petrov, V.1    Scott, S.K.2    Showalter, K.3
  • 32
    • 0001102631 scopus 로고
    • Complex patterns in a simple system
    • Pearson J E 1994 Complex patterns in a simple system Science 261 189-92
    • (1994) Science , vol.261 , pp. 189-192
    • Pearson, J.E.1
  • 33
    • 0000838693 scopus 로고    scopus 로고
    • Dynamics of self-replicating spots in reaction-diffusion systems
    • Reynolds J, Pearson J and Ponce-Dawson S 1997 Dynamics of self-replicating spots in reaction-diffusion systems Phys. Rev. E 56 185-98
    • (1997) Phys. Rev. E , vol.56 , pp. 185-198
    • Reynolds, J.1    Pearson, J.2    Ponce-Dawson, S.3
  • 34
    • 0001360757 scopus 로고
    • Dynamics of self-replicating patterns in reaction diffusion systems
    • Reynolds J, Pearson J and Ponce-Dawson S 1994 Dynamics of self-replicating patterns in reaction diffusion systems Phys. Rev. Lett. 72 2797-800
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 2797-2800
    • Reynolds, J.1    Pearson, J.2    Ponce-Dawson, S.3
  • 35
  • 36
    • 21144478287 scopus 로고
    • On the existence of multiple single-peaked solutions for a semilinear Neumann problem
    • Wang Z-Q 1992 On the existence of multiple single-peaked solutions for a semilinear Neumann problem Arch. Rational Mech. Anal. 120 375-99
    • (1992) Arch. Rational Mech. Anal. , vol.120 , pp. 375-399
    • Wang, Z.-Q.1
  • 37
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem
    • Wei J 1996 On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Diff. Eqn. 129 315-33
    • (1996) J. Diff. Eqn. , vol.129 , pp. 315-333
    • Wei, J.1
  • 38
    • 0031562011 scopus 로고    scopus 로고
    • On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem
    • Wei J 1997 On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem J. Differ. Eqns. 134 104-33
    • (1997) J. Differ. Eqns. , vol.134 , pp. 104-133
    • Wei, J.1
  • 40
    • 0009233822 scopus 로고    scopus 로고
    • Multiple boundary spike solutions for a wide class of singular perturbation problems
    • to appear
    • Wei J and Winter M Multiple boundary spike solutions for a wide class of singular perturbation problems J. Lond. Math. Soc. to appear
    • J. Lond. Math. Soc.
    • Wei, J.1    Winter, M.2
  • 41
    • 0347188202 scopus 로고    scopus 로고
    • On the interior spike layer solutions for some singular perturbation problems
    • Wei J 1998 On the interior spike layer solutions for some singular perturbation problems Proc. R. Soc. Edinburgh A (Mathematics) A 128 849-74
    • (1998) Proc. R. Soc. Edinburgh A (Mathematics) A , vol.128 , pp. 849-874
    • Wei, J.1
  • 42
    • 0032398054 scopus 로고    scopus 로고
    • On the interior spike layer solutions of singularly perturbed semilinear Neumann problem
    • Wei J 1998 On the interior spike layer solutions of singularly perturbed semilinear Neumann problem Tohoku Math. J. 50 159-78
    • (1998) Tohoku Math. J. , vol.50 , pp. 159-178
    • Wei, J.1
  • 44
    • 0009233823 scopus 로고    scopus 로고
    • On single interior spike solutions of Gierer-Meinhardt system: Uniqueness, spectrum estimates and stability analysis
    • to appear
    • Wei J On single interior spike solutions of Gierer-Meinhardt system: uniqueness, spectrum estimates and stability analysis Euro. J. Appl. Math. to appear
    • Euro. J. Appl. Math.
    • Wei, J.1


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