Global solutions for a general strongly coupled prey–predator model☆

作者: Huiling Li , Peter YH Pang , Mingxin Wang , None

DOI: 10.1016/J.AML.2008.06.050

关键词:

摘要: Abstract This work investigates global solutions for a general strongly coupled prey–predator model that involves (self-)diffusion and cross-diffusion, where the cross-diffusion is of form v / ( 1 + u l ) with ≥ . Very few mathematical results are known such models, especially in higher spatial dimensions.

参考文章(15)
Dung Le, Cross diffusion systems on n spatial dimensional domains Indiana University Mathematics Journal. ,vol. 51, pp. 625- 643 ,(2002) , 10.1512/IUMJ.2002.51.2198
Emmanuele DiBenedetto, Degenerate Parabolic Equations ,(1993)
Herbert Amann, Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems Differential and Integral Equations. ,vol. 3, pp. 13- 75 ,(1990)
Peter Y. H. Pang, Mingxin Wang, Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion Proceedings of The London Mathematical Society. ,vol. 88, pp. 135- 157 ,(2004) , 10.1112/S0024611503014321
Y. S. Choi, , Roger Lui, Yoshio Yamada, , , Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion Discrete and Continuous Dynamical Systems. ,vol. 10, pp. 719- 730 ,(2004) , 10.3934/DCDS.2004.10.719
Yuan Lou, , Wei-Ming Ni, Yaping Wu, , , On the global existence of a cross-diffusion system Discrete and Continuous Dynamical Systems. ,vol. 4, pp. 193- 203 ,(1998) , 10.3934/DCDS.1998.4.193
Y. S. Choi, , Roger Lui, Yoshio Yamada, , , Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion Discrete and Continuous Dynamical Systems. ,vol. 9, pp. 1193- 1200 ,(2003) , 10.3934/DCDS.2003.9.1193
P. Y. H. Pang, M. X. Wang, Existence of global solutions for a three‐species predator‐prey model with cross‐diffusion Mathematische Nachrichten. ,vol. 281, pp. 555- 560 ,(2008) , 10.1002/MANA.200510624
Seong-A Shim, Uniform Boundedness and Convergence of Solutions to Cross-Diffusion Systems Journal of Differential Equations. ,vol. 185, pp. 281- 305 ,(2002) , 10.1006/JDEQ.2002.4169
Xinfu Chen, Yuanwei Qi, Mingxin Wang, A strongly coupled predator–prey system with non-monotonic functional response ☆ Nonlinear Analysis-theory Methods & Applications. ,vol. 67, pp. 1966- 1979 ,(2007) , 10.1016/J.NA.2006.08.022