Uniqueness and stability of steady states for a predator-prey model in heterogeneous environment
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- by Rui Peng and Mingxin Wang PDF
- Proc. Amer. Math. Soc. 136 (2008), 859-865 Request permission
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
- Yihong Du and Sze-Bi Hsu, A diffusive predator-prey model in heterogeneous environment, J. Differential Equations 203 (2004), no. 2, 331–364. MR 2073690, DOI 10.1016/j.jde.2004.05.010
- Yihong Du and Qingguang Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal. 31 (1999), no. 1, 1–18. MR 1720128, DOI 10.1137/S0036141099352844
- Yihong Du and Mingxin Wang, Asymptotic behaviour of positive steady states to a predator-prey model, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), no. 4, 759–778. MR 2250444, DOI 10.1017/S0308210500004704
- Julián López-Gómez and Rosa M. Pardo, Invertibility of linear noncooperative elliptic systems, Nonlinear Anal. 31 (1998), no. 5-6, 687–699. MR 1487855, DOI 10.1016/S0362-546X(97)00640-8
- Yuan Lou and Wei-Ming Ni, Diffusion vs cross-diffusion: an elliptic approach, J. Differential Equations 154 (1999), no. 1, 157–190. MR 1685622, DOI 10.1006/jdeq.1998.3559
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
- MR Author ID: 728442
- Email: pengrui_seu@163.com
- Mingxin Wang
- Affiliation: Department of Mathematics, Southeast University, Nanjing City, 210018, People’s Republic of China
- Received by editor(s): December 15, 2005
- Received by editor(s) in revised form: April 9, 2006
- Published electronically: 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 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 859-865
- MSC (2000): Primary 35J20, 35J60
- DOI: https://doi.org/10.1090/S0002-9939-07-09061-2
- MathSciNet review: 2361857