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Uniqueness and stability of steady states for a predator-prey model in heterogeneous environment
Author(s):
Rui
Peng;
Mingxin
Wang
Journal:
Proc. Amer. Math. Soc.
136
(2008),
859-865.
MSC (2000):
Primary 35J20, 35J60
Posted:
November 26, 2007
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Abstract:
In this paper, we deal with a predator-prey model with diffusion in a heterogeneous environment, and we study the uniqueness and stability of positive steady states as the diffusion coefficient of the predator is small enough.
References:
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- 1.
- Y. H. Du and S. B. Hsu, A diffusive predator-prey model in heterogeneous environment, J. Diff. Equns., 203(2004), 331-364. MR 2073690 (2005e:35051)
- 2.
- Y. H. Du and Q. G. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal., 31(1999), 1-18. MR 1720128 (2000g:35059)
- 3.
- Y. H. Du and M. X. Wang, Asymptotic behavior of positive steady-states to a predator-prey model, Proc. Roy. Soc. Edinburgh Sect. A, 136(2006), 759-778. MR 2250444
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Invertiblility of linear noncooperative elliptic systems, Nonlinear Anal., TMA, 31(1998), 687-699. MR 1487855 (99b:34046) - 5.
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Additional Information:
Rui
Peng
Affiliation:
Institute of Nonlinear Complex System, College of Science, China Three Gorges University, Yichang City, 443002, Hubei Province, People's Republic of China
Email:
pengrui_seu@163.com
Mingxin
Wang
Affiliation:
Department of Mathematics, Southeast University, Nanjing City, 210018, People's Republic of China
DOI:
10.1090/S0002-9939-07-09061-2
PII:
S 0002-9939(07)09061-2
Keywords:
Predator-prey model,
steady state,
uniqueness,
stability.
Received by editor(s):
December 15, 2005
Received by editor(s) in revised form:
April 9, 2006
Posted:
November 26, 2007
Additional Notes:
The work of R. Peng was partially supported by the Scientific Research Projects of Hubei Provincial Department of Education Q200713001, and the work of M. X. Wang was partially supported by the National Science Foundation of China 10771032.
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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