Citation: |
[1] |
I. Averill, Y. Lou and D. Munther, On several conjectures from evolution of dispersal, J. Biol. Dyn., in press. |
[2] |
F. Belgacem, "Elliptic Boundary Value Problems with Indefinite Weights: Variational Formulations of the Principal Eigenvalue and Applications," Pitman Res. Notes Math. Ser., 368, Longman Sci, 1997. |
[3] |
F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Appl. Math. Quarterly, 3 (1995), 379-397. |
[4] |
N. P. Bhatia and G. P. Szegö, "Stability Theory of Dynamical Systems," Springer-Verlag, New York, 1970. |
[5] |
R. S. Cantrell and C. Cosner, Practical persistence in ecological models via comparison methods, Proc. Roy. Soc. Edinb. A, 126 (1996), 247-272.doi: 10.1017/S0308210500022721. |
[6] |
R. S. Cantrell and C. Cosner, "Spatial Ecology via Reaction-Diffusion Equations," Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003. |
[7] |
R. S. Cantrell, C. Cosner and Y. Lou, Advection mediated coexistence of competing species, Proc. Roy. Soc. Edinb. A, 137 (2007), 497-518. |
[8] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolution of dispersal and the ideal free distribution, Math. Bios. Eng., 7 (2010), 17-36.doi: 10.3934/mbe.2010.7.17. |
[9] | |
[10] |
X. F. Chen and Y. Lou, Principal eigenvalue and eigenfunction of an elliptic operator with large convection and its application to a competition model, Indiana Univ. Math. J., 57 (2008), 627-658.doi: 10.1512/iumj.2008.57.3204. |
[11] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal., 8 (1971), 321-340.doi: 10.1016/0022-1236(71)90015-2. |
[12] |
J. Dockery, V. Hutson, K. Mischaikow and M. Pernarowski, The evolution of slow dispersal rates: A reaction-diffusion model, J. Math. Biol., 37 (1998), 61-83.doi: 10.1007/s002850050120. |
[13] |
S. D. Fretwell and H. L. Lucas, On territorial behavior and other factors influencing habitat selection in birds: Theoretical development, Acta Biotheor., 19 (1970), 16-36.doi: 10.1007/BF01601953. |
[14] |
A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, 1964. |
[15] |
R. Gejji, Y. Lou, D. Munther and J. Peyton, Evolutionary convergence to ideal free dispersal strategies and coexistence, Bull. Math. Biol., 74 (2012), 257-299.doi: 10.1007/s11538-011-9662-4. |
[16] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equation of Second Order," 2^{nd} edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 224, Springer-Verlag, Berlin, 1983. |
[17] |
J. K. Hale, Dynamical systems and stability, J. Math. Anal. Appl., 26 (1969), 39-59.doi: 10.1016/0022-247X(69)90175-9. |
[18] |
G. H. Hardy, J. E. Littlewood and G. Pólya, "Inequalities," University Press, Cambridge, UK, 1952. |
[19] |
A. Hastings, Can spatial variation alone lead to selection for dispersal?, Theor. Pop. Biol., 24 (1983), 244-251.doi: 10.1016/0040-5809(83)90027-8. |
[20] |
P. Hess, "Periodic-Parabolic Boundary Value Problems and Positivity," Pitman Res. Notes Math. Ser., 247, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
[21] |
J. Huska, Harnack inequality and exponential separation for oblique derivative problems on Lipschitz domains, Journal of Differential Equations, 226 (2006), 541-557. |
[22] |
K. Y. Lam, Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model, J. Differential Equations, 250 (2011), 161-181. |
[23] |
K. Y. Lam, Limiting profiles of semilinear elliptic equations with large advection in population dynamics, II,, SIAM J. Math Anal., in press. |
[24] |
K. Y. Lam and W. M. Ni, Limiting profiles of semilinear elliptic equations with large advection in population dynamics, Discrete Contin. Dynam. Syst., 28 (2010), 1051-1067.doi: 10.3934/dcds.2010.28.1051. |
[25] |
Y. Lou, On the effects of migration and spatial heterogeneity on single and multiple species, Journal of Differential Equations, 223 (2006), 400-426. |
[26] |
W.-M. Ni, "The Mathematics of Diffusion," CBMS-NSF Regional Conference Series in Applied Mathematics, 82, SIAM, 2011. |
[27] |
A. Okubo and S. A. Levin, "Diffusion and Ecological Problems: Modern Perspectives, Interdisciplinary Applied Mathematics," Vol. 14, 2^{nd} edition, Springer, Berlin, 2001. |
[28] |
M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations," 2^{nd} edition, Springer-Verlag, Berlin, 1984. |
[29] |
R. Redlinger, Über die $C^2$-kompaktheit der bahn der lösungen semilinearer parabolischer systeme, Proc. Roy. Soc. Edinb. A, 93 (1983), 99-103.doi: 10.1017/S0308210500031693. |
[30] |
N. Shigesada and K. Kawasaki, "Biological Invasions: Theory and Practice," Oxford Series in Ecology and Evolution, Oxford University Press, Oxford, New York, Tokyo, 1997. |
[31] |
H. Smith, "Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems," Mathematical Surveys and Monographs, 41, American Mathematical Society, Providence, RI, 1995. |
[32] |
P. Turchin, "Qualitative Analysis of Movement," Sinauer Press, Sunderland, MA, 1998. |
[33] |
E. Zeidler, "Nonlinear Functional Analysis and its Applications. I. Fixed Point Theorems," Springer-Verlag, New York, 1985. |