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http://dx.doi.org/10.14317/jami.2011.29.1_2.075

EXISTENCE OF GLOBAL SOLUTIONS FOR A PREY-PREDATOR MODEL WITH NON-MONOTONIC FUNCTIONAL RESPONSE AND CROSS-DIFFUSION  

Xu, Shenghu (Department of Mathematics, Longdong University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.1_2, 2011 , pp. 75-85 More about this Journal
Abstract
In this paper, using the energy estimates and the bootstrap arguments, the global existence of classical solutions for a prey-predator model with non-monotonic functional response and cross-diffusion where the prey and predator both have linear density restriction is proved when the space dimension n < 10.
Keywords
Cross-diffusion; Classical solutions; Non-monotonic; functional response;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Y. S. Choi, R. Lui and Y. Yamada, Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion, Discrete Contin. Dynam. Systems10(2004), 719-730.
2 P. V. Tuoc, On global existence of solutions to a cross-diffusion system. J. Math. Anal. Appl343(2008), 826-834.   DOI   ScienceOn
3 O. A. Ladyzenskaja and V. A. Solonnikov, N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, AMS, 1968.
4 A. Shim, $W\frac{1}{2}$-estimates on the prey-predator systems with cross-diffusions and functional responses. Commun. Keorean. Math. Soc23(2008), 211-227.   DOI
5 H. Amann, Dynamic theory of quasilinear parabolic equations: Global existence, Math. Z 202(1989), 219-250.   DOI   ScienceOn
6 N. Shigesada, K. Kawasaki and E. Teramoto, Spatial segregation of interacting species. J. Theor. Biology79(1979), 83-99.   DOI   ScienceOn
7 Y. S. Choi, R. Lui and Y. Yamada, Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion. Discrete Contin. Dynam. Systems9(2003), 1193-1200.
8 W. Ko and K. Ryu, coexistence states of a predator-prey system with non-monotonic functional response, Nonlinear Analysis: RWA8(2007), 769-786.   DOI   ScienceOn
9 H. Amann, Dynamic theory of quasilinear parabolic equations: Abstract evolution equations, Nonlinear Analysis12(1988), 859-919.
10 H. Amann, Dynamic theory of quasilinear parabolic equations: Reaction-diffusion, Diff. Int. Eqs3(1990), 13-75.
11 X. F. Chen, Y. W. Qi and M. X. Wang, A Strongly coupled predator-prey system with non-monotonic functional response, Nonlinear Analysis: RWA 67(2007), 1966-1979.   DOI   ScienceOn
12 H. Zhu, S. Campbell and G. Wolkowicz, Bifurcation analysis of a predatorCprey system with nonmonotonic functional response, SIAM J. Appl. Math63(2) (2002), 636C682.
13 C. Holing, The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Ent, Soc. Can 45(1965), 1-65.
14 W. Ko and K. Ryu, A qualitative study on general Gause-type predator-prey models with non-monotonic functional response, Nonlinear Analysis: RWA 10(4)(2009), 2558-2573.   DOI   ScienceOn
15 J. F. Andrews, A mathematical model for the continuous culture of microoganisms utilizing inhibitorysubstrates, Biotech. Bioeng10(1968), 707-723.   DOI
16 S. H. Xu, Existence of global solutions for a predator-prey model with cross-diffusion, Electronic. J. Diff. Eqns 06(2008), 1-14.
17 S. Ruan and D. Xiao, Global analysis in a predatorCprey system with nonmonotonic functional response, SIAM J. Appl. Math61(4)(2000), 1445C1472.