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Preface
The periodic patch model for population dynamics with fractional diffusion
1. | Ecole des Hautes Etudes en Sciences Sociales, CAMS, 54, bd Raspail F-75270 Paris, France |
2. | Institut de Mathématiques, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 4, France |
3. | Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63 - 35121 Padova, Italy |
References:
[1] |
H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques, J. Funct. Anal, 40 (1981), 1-29.
doi: doi:10.1016/0022-1236(81)90069-0. |
[2] |
H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.
doi: doi:10.1007/s00220-004-1201-9. |
[3] |
H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol, 51 (2005), 75-113.
doi: doi:10.1007/s00285-004-0313-3. |
[4] |
H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating travelling fronts, J. Math. Pures Appl, 84 (2005), 1101-1146.
doi: doi:10.1016/j.matpur.2004.10.006. |
[5] |
J.-M. Bony, P. Courrège and P. Priouret, Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum, Ann. Inst. Fourier, 18 (1968), 369-521. |
[6] |
X. Cabré and J.-M. Roquejoffre, Propagation de fronts dans les équations de Fisher-KPP avec diffusion fractionnaire, C. R. Math. Acad. Sci. Paris, 347 (2009), 1361-1366. |
[7] |
Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift, Proc. Royal Soc. Edinburgh, 132 (2002), 567-594.
doi: doi:10.1017/S0308210500001785. |
[8] |
P. Constantin, A. Kiselev, L. Ryzhik and A. Zlatos, Diffusion and mixing in fluid flow, Annals of Math., 168 (2008), 643-674.
doi: doi:10.4007/annals.2008.168.643. |
[9] | |
[10] |
P. C. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Springer-Verlag, 1979. |
[11] |
A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, Etude de l'équation de diffusion avec accroissement de la quantité de matière, et son application à un problème biologique, Bjul. Moskowskogo Gos. Univ., 17 (1937), 1-26. |
[12] |
J. D. Murray, "Mathematical Biology," 2nd edition, Biomathematics, 19, Springer-Verlag, Berlin, 1993. |
show all references
References:
[1] |
H. Berestycki, Le nombre de solutions de certains problèmes semi-linéaires elliptiques, J. Funct. Anal, 40 (1981), 1-29.
doi: doi:10.1016/0022-1236(81)90069-0. |
[2] |
H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.
doi: doi:10.1007/s00220-004-1201-9. |
[3] |
H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol, 51 (2005), 75-113.
doi: doi:10.1007/s00285-004-0313-3. |
[4] |
H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating travelling fronts, J. Math. Pures Appl, 84 (2005), 1101-1146.
doi: doi:10.1016/j.matpur.2004.10.006. |
[5] |
J.-M. Bony, P. Courrège and P. Priouret, Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum, Ann. Inst. Fourier, 18 (1968), 369-521. |
[6] |
X. Cabré and J.-M. Roquejoffre, Propagation de fronts dans les équations de Fisher-KPP avec diffusion fractionnaire, C. R. Math. Acad. Sci. Paris, 347 (2009), 1361-1366. |
[7] |
Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift, Proc. Royal Soc. Edinburgh, 132 (2002), 567-594.
doi: doi:10.1017/S0308210500001785. |
[8] |
P. Constantin, A. Kiselev, L. Ryzhik and A. Zlatos, Diffusion and mixing in fluid flow, Annals of Math., 168 (2008), 643-674.
doi: doi:10.4007/annals.2008.168.643. |
[9] | |
[10] |
P. C. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Springer-Verlag, 1979. |
[11] |
A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, Etude de l'équation de diffusion avec accroissement de la quantité de matière, et son application à un problème biologique, Bjul. Moskowskogo Gos. Univ., 17 (1937), 1-26. |
[12] |
J. D. Murray, "Mathematical Biology," 2nd edition, Biomathematics, 19, Springer-Verlag, Berlin, 1993. |
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