Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model

Journal of Differential Equations

Volumn 250, Issue 1, 2011, Pages 161-181

  Lam, King Yeung ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Concentration phenomenon; Large advection; Limiting profile; Mathematical ecology; Primary; Secondary

Indexed keywords

EID: 78149284100     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2010.08.028     Document Type: Article

References (20)

1. Cantrell R.S., Cosner C. Spatial Ecology via Reaction-Diffusion Equations. Wiley Ser. Math. Comput. Biol. 2003.
2. Levin S. Population models and community structure in heterogeneous environments. Biomath. 1986, vol. 17. Springer-Verlag, Berlin. T.G. Hallam, S. Levin (Eds.).
3. Okubo A. Diffusion and Ecological Problems: Mathematical Models. Biomath. 1980, vol. 10. Springer-Verlag, Berlin.
4. Skellam J.G. Random dispersal in theoretical populations. Biometrika 1951, 38:196-218.
5. Cantrell R.S., Cosner C. The effects of spatial heterogeneity in population dynamics. J. Math. Biol. 1991, 29:315-338.
6. Belgacem F., Cosner C. The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment. Can. Appl. Math. Q. 1995, 3:379-397.
7. Belgacem F. Elliptic Boundary Value Problems with Indefinite Weights: Variational Formulations of the Principal Eigenvalue and Applications. Pitman Res. Notes Math. Ser. 1997, vol. 368. Longman, Harlow.
8. Cosner C., Lou Y. Does movement toward better environments always benefit a population?. J. Math. Anal. Appl. 2003, 277:489-503.
9. Cantrell R.S., Cosner C., Lou Y. Advection-mediated coexistence of competing species. Proc. Roy. Soc. Edinburgh Sect. A 2007, 137:497-518.
10. Lou Y. Some challenging mathematical problems in evolution of dispersal and population dynamics. Lecture Notes in Math. 2008, vol. 1922:171-205. Springer-Verlag, Berlin.
11. Chen X., Lou Y. Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model. Indiana Univ. Math. J. 2008, 57:627-657.
12. Cantrell R.S., Cosner C., Lou Y. Movement toward better environments and the evolution of rapid diffusion. Math. Biosci. 2006, 204:199-214.
13. Dockery J., Hutson V., Mischaikow K., Pernarowski M. The evolution of slow dispersal rates: A reaction-diffusion model. J. Math. Biol. 1998, 37:61-83.
14. Sattinger D.H. Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J. 1972, 21:979-1000.
15. Du Y. Order Structure and Topological Methods in Nonlinear Partial Differential Equations, vol. 1 2006, World Scientific.
16. Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Grundlehren Math. Wiss. 1983, vol. 224. Springer-Verlag, Berlin.
17. Berestycki H., Caffarelli L., Nirenberg L. Further qualitative properties for elliptic equations in unbounded domains. Ann. Sc. Norm. Super. Pisa Cl. Sci. 1997, XXV:69-94.
18. Lam K.Y., Ni W.M. Limiting profiles of semilinear elliptic equations with large advection in population dynamics. Discrete Contin. Dyn. Syst. 2009, 28(3):1051-1067.
19. Bezuglyy A., Lou Y. Reaction-diffusion models with large advection coefficients. Appl. Anal. 2010, 89:983-1004.
20. Y. Lou, Private communication, 2009.