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Reaction diffusion equation with non-local term arises as a mean field limit of the master equation
1. | The Institute of Medical Science, The University of Tokyo, 4-6-1 Shirokanedai Minato-ku, Tokyo, 108-8639, Japan |
2. | Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho, Toyonakashi, 560-8531, Japan |
3. | Japan Science and Technology Agency, CREST 5, Sanbancho, Chiyoda-ku, Tokyo, 102-0075, Japan |
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J. D. Murray, "Mathematical Biology I: An Introduction," 3rd edition, Interdisciplinary Applied Mathematics, 17, Springer-Verlag, New York, 2001. |
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A. Okubo, "Diffusion and Ecological Problems: Modern Perspectives," 2nd edition edition, Interdisciplinary Applied Mathematics, 14, Springer-Verlag, New York, 2001. |
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H. G. Othmer, S. R. Dumber and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298.
doi: 10.1007/BF00277392. |
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doi: 10.1137/S0036139995288976. |
show all references
References:
[1] |
P. A. Egelstaff, "An Introduction to the Liquid State," Academic Press, London, 1967. |
[2] |
J. D. Murray, "Mathematical Biology I: An Introduction," 3rd edition, Interdisciplinary Applied Mathematics, 17, Springer-Verlag, New York, 2001. |
[3] |
A. Okubo, "Diffusion and Ecological Problems: Modern Perspectives," 2nd edition edition, Interdisciplinary Applied Mathematics, 14, Springer-Verlag, New York, 2001. |
[4] |
H. G. Othmer, S. R. Dumber and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298.
doi: 10.1007/BF00277392. |
[5] |
H. G. Othmer and A. Stevens, Aggregation, blowup, and collapse: The ABCs of taxis in reinforced random walks, SIAM J. Appl. Math., 57 (1997), 1044-1081.
doi: 10.1137/S0036139995288976. |
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