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On the Hollman McKenna conjecture: Interior concentration near curves
Exact multiplicity of stationary limiting problems of a cell polarization model
| 1. | Center for PDE, East China Normal University, Minhang, Shanghai 200241, China |
| 2. | Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan |
| 3. | Faculty of Engineering, University of Miyazaki, Miyazaki, 889-2192 |
| 4. | Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, Shiga 520-2194 |
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K. Kuto and T. Tsujikawa, Stationary patterns for an adsorbate-induced phase transition model II, Nonlinearity, 26 (2013), 1313-1343.
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K. Kuto and T. Tsujikawa, Bifurcation structure of steady-states for bistable equations with nonlocal constraint, Discrete and Continuous Dynamical Systems Supplement, (2013), 467-476.
doi: 10.3934/proc.2013.2013.467. |
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T.Mori, K.Kuto, T.Tujikawa, M.Nagayama and S.Yotsutani, Global bifurcation sheet and diagrams of wave-pinning in a reaction-diffusion model for cell polarization, Dynamical Systems, Differential Equations and Applications AIMS Proceedings, 2015, 861-877.
doi: 10.3934/proc.2015.0861. |
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Y. Mori A. Jilkine and L. Edelstein-Keshet, Wave-pinning and cell polarity from a bistable reaction-diffusion system, Biophys J., 94 (2008), 3684-3697. |
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Y. Mori, A. Jilkine and L. Edelstein-Keshet, Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization, SIAM J. Appl. Math., 71 (2011), 1401-1427.
doi: 10.1137/10079118X. |
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J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer, 1994.
doi: 10.1007/978-1-4612-0873-0. |
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J. Smoller and A. Wasserman, Global bifurcation of steady-state solutions, J. Differential Equations, 39 (1981), 269-290.
doi: 10.1016/0022-0396(81)90077-2. |
show all references
References:
| [1] |
J. Carr, M. E. Gurtin and M. Semrod, Structured phase transitions on a finite interval, Arch. Rational Mech. Anal., 86 (1984), 317-351.
doi: 10.1007/BF00280031. |
| [2] |
S. Kosugi Y. Morita and S. Yotsutani, Stationary solutions to the one-dimensional Cahn-Hilliard equation: Proof by the complete elliptic integrals, Discrete and Continuous Dynamical Systems, 19 (2007), 609-629.
doi: 10.3934/dcds.2007.19.609. |
| [3] |
K. Kuto and T. Tsujikawa, Stationary patterns for an adsorbate-induced phase transition model I, Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), 1105-1117.
doi: 10.3934/dcdsb.2010.14.1105. |
| [4] |
K. Kuto and T. Tsujikawa, Stationary patterns for an adsorbate-induced phase transition model II, Nonlinearity, 26 (2013), 1313-1343.
doi: 10.1088/0951-7715/26/5/1313. |
| [5] |
K. Kuto and T. Tsujikawa, Bifurcation structure of steady-states for bistable equations with nonlocal constraint, Discrete and Continuous Dynamical Systems Supplement, (2013), 467-476.
doi: 10.3934/proc.2013.2013.467. |
| [6] |
Y. Lou, W.-M. Ni and S. Yotsutani, On a limiting system in the Lotka-Voltera competition with cross diffusion, Discrete Contin. Dyn. Syst., 10 (2004), 435-458.
doi: 10.3934/dcds.2004.10.435. |
| [7] |
T.Mori, K.Kuto, T.Tujikawa, M.Nagayama and S.Yotsutani, Global bifurcation sheet and diagrams of wave-pinning in a reaction-diffusion model for cell polarization, Dynamical Systems, Differential Equations and Applications AIMS Proceedings, 2015, 861-877.
doi: 10.3934/proc.2015.0861. |
| [8] |
Y. Mori A. Jilkine and L. Edelstein-Keshet, Wave-pinning and cell polarity from a bistable reaction-diffusion system, Biophys J., 94 (2008), 3684-3697. |
| [9] |
Y. Mori, A. Jilkine and L. Edelstein-Keshet, Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization, SIAM J. Appl. Math., 71 (2011), 1401-1427.
doi: 10.1137/10079118X. |
| [10] |
J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer, 1994.
doi: 10.1007/978-1-4612-0873-0. |
| [11] |
J. Smoller and A. Wasserman, Global bifurcation of steady-state solutions, J. Differential Equations, 39 (1981), 269-290.
doi: 10.1016/0022-0396(81)90077-2. |
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