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A vanishing diffusion limit in a nonstandard system of phase field equations
An integration model for two different ethnic groups
1. | Department of Mathematics, University of Bologna, Italy |
2. | LNCC, Petropolis, Brazil |
References:
[1] |
C. Argyris and D. Schon, Organizational Learning: A Theory of Action Perspective 22, Park: Addison-Wesley, 1978. |
[2] |
J. W. Barrett and J. F. Blowey, Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, Math. Comp., 68 (1999), 487-517.
doi: 10.1090/S0025-5718-99-01015-7. |
[3] |
A. Berti and I. Bochicchio, A mathematical model for phase separation: A generalized Cahn-Hilliard equation, Math. Meth. Appl. Sci., 34 (2011), 1193-1201.
doi: 10.1002/mma.1432. |
[4] |
L. Bevilacqua, A. C. Galeão, F. Pietrobon-Costa and S. L. Monteiro, Knowledge diffusion paths in a research chain, Mecânica Computacional, 24 (2010), 2061-2069. |
[5] |
H. P. Boswijk and P. H. Franses, On the econometrics of the bass diffusion model, Journal of Business & Economic Statistics, 23 (2005), 255-268.
doi: 10.1198/073500104000000604. |
[6] |
V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Physica D, 236 (2007), 13-21.
doi: 10.1016/j.physd.2007.07.009. |
[7] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy, J. Chem. Phys, 28 (1958), 258-267.
doi: 10.1063/1.1744102. |
[8] |
J. W. Cahn, C. M. Elliott and A. Novik-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion of minus Laplacian of the mean curvature, European J. Appl. Math., 7 (1996), 287-301.
doi: 10.1017/S0956792500002369. |
[9] |
L. L. Cavalli-Sforza and M. Feldman, Cultural Transmission and Evolution, Princeton University Press, Princeton, 1981. |
[10] |
E. Collett, Immigrant Integration in Europe in a Time of Austerity, Migration Policy Institute, Washington, 2011. |
[11] |
M. Fabrizio, C. Giorgi and A. Morro, A continuum theory for first-order phase transitions based on the balance of structure order, Math. Meth. Appl. Sci., 31 (2008), 627-653.
doi: 10.1002/mma.930. |
[12] |
M. Fabrizio, C. Giorgi and A. Morro, Phase separation in quasi-incompressible Cahn-Hilliard fluids, European Journal of Mechanics B/Fluids, 30 (2011), 281-287.
doi: 10.1016/j.euromechflu.2010.12.003. |
[13] |
M. Fabrizio, B. Lazzari and R. Nibbi, Thermodynamics of non-local materials: Extra fluxes and internal powers, Continuum Mech. Thermodyn, 23 (2011), 509-525.
doi: 10.1007/s00161-011-0193-x. |
[14] |
M. Gladwell, The Tipping Point. How little things can make a big difference, Little Brown and Company, London, 2000. |
[15] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[16] |
J. He, Knowledge management and knowledge fermentation, Science of Science and Management of S.&.T., 25 (2004), 23-26. |
[17] |
G. Hedlund, A model of knowledge management and the N-Form corporation, Strategic Management Journal, 15 (1994), 73-90.
doi: 10.1002/smj.4250151006. |
[18] |
Z. Li, T. Zhu and W. Lai, A Study on the knowledge diffusion of communities of practice based on the weighted small-world network, Journal of Computers, 5 (2010), 1046-1053.
doi: 10.4304/jcp.5.7.1046-1053. |
[19] |
R. McAdam, Knowledge creation and idea generations critical quality perspective, Technovation, 24 (2004), 697-705. |
[20] |
I. Nonaka and N Konno, The concept of Ba: Building a foundation for knowledge creation, California Management Review, 40 (1998), 40-54.
doi: 10.2307/41165942. |
[21] |
Z. Shaoying, The model of dynamic spread knowledge based on organizational learning, Science Research Management, 24 (2003), 67-71. |
show all references
References:
[1] |
C. Argyris and D. Schon, Organizational Learning: A Theory of Action Perspective 22, Park: Addison-Wesley, 1978. |
[2] |
J. W. Barrett and J. F. Blowey, Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, Math. Comp., 68 (1999), 487-517.
doi: 10.1090/S0025-5718-99-01015-7. |
[3] |
A. Berti and I. Bochicchio, A mathematical model for phase separation: A generalized Cahn-Hilliard equation, Math. Meth. Appl. Sci., 34 (2011), 1193-1201.
doi: 10.1002/mma.1432. |
[4] |
L. Bevilacqua, A. C. Galeão, F. Pietrobon-Costa and S. L. Monteiro, Knowledge diffusion paths in a research chain, Mecânica Computacional, 24 (2010), 2061-2069. |
[5] |
H. P. Boswijk and P. H. Franses, On the econometrics of the bass diffusion model, Journal of Business & Economic Statistics, 23 (2005), 255-268.
doi: 10.1198/073500104000000604. |
[6] |
V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Physica D, 236 (2007), 13-21.
doi: 10.1016/j.physd.2007.07.009. |
[7] |
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial energy, J. Chem. Phys, 28 (1958), 258-267.
doi: 10.1063/1.1744102. |
[8] |
J. W. Cahn, C. M. Elliott and A. Novik-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: Motion of minus Laplacian of the mean curvature, European J. Appl. Math., 7 (1996), 287-301.
doi: 10.1017/S0956792500002369. |
[9] |
L. L. Cavalli-Sforza and M. Feldman, Cultural Transmission and Evolution, Princeton University Press, Princeton, 1981. |
[10] |
E. Collett, Immigrant Integration in Europe in a Time of Austerity, Migration Policy Institute, Washington, 2011. |
[11] |
M. Fabrizio, C. Giorgi and A. Morro, A continuum theory for first-order phase transitions based on the balance of structure order, Math. Meth. Appl. Sci., 31 (2008), 627-653.
doi: 10.1002/mma.930. |
[12] |
M. Fabrizio, C. Giorgi and A. Morro, Phase separation in quasi-incompressible Cahn-Hilliard fluids, European Journal of Mechanics B/Fluids, 30 (2011), 281-287.
doi: 10.1016/j.euromechflu.2010.12.003. |
[13] |
M. Fabrizio, B. Lazzari and R. Nibbi, Thermodynamics of non-local materials: Extra fluxes and internal powers, Continuum Mech. Thermodyn, 23 (2011), 509-525.
doi: 10.1007/s00161-011-0193-x. |
[14] |
M. Gladwell, The Tipping Point. How little things can make a big difference, Little Brown and Company, London, 2000. |
[15] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[16] |
J. He, Knowledge management and knowledge fermentation, Science of Science and Management of S.&.T., 25 (2004), 23-26. |
[17] |
G. Hedlund, A model of knowledge management and the N-Form corporation, Strategic Management Journal, 15 (1994), 73-90.
doi: 10.1002/smj.4250151006. |
[18] |
Z. Li, T. Zhu and W. Lai, A Study on the knowledge diffusion of communities of practice based on the weighted small-world network, Journal of Computers, 5 (2010), 1046-1053.
doi: 10.4304/jcp.5.7.1046-1053. |
[19] |
R. McAdam, Knowledge creation and idea generations critical quality perspective, Technovation, 24 (2004), 697-705. |
[20] |
I. Nonaka and N Konno, The concept of Ba: Building a foundation for knowledge creation, California Management Review, 40 (1998), 40-54.
doi: 10.2307/41165942. |
[21] |
Z. Shaoying, The model of dynamic spread knowledge based on organizational learning, Science Research Management, 24 (2003), 67-71. |
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