Báo cáo hóa học: "Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 654539 19 pages doi 2009 654539 Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-II The Case in R1 Rui Zhang 1 2 Ling Guo 1 and Shengmao Fu1 1 Department of Mathematics Northwest Normal University Lanzhou 730070 China 2 Department of Mathematics Lanzhou Jiaotong University Lanzhou 730070 China Correspondence should be addressed to Shengmao Fu fusm@ Received 2 April 2009 Accepted 31 August 2009 Recommended by Wenming Zou A Holling type III predator-prey model with self- and cross-population pressure is considered. Using the energy estimate and Gagliardo-Nirenberg-type inequalities the existence and uniform boundedness of global solutions to the model are dicussed. In addition global asymptotic stability of the positive equilibrium point for the model is proved by Lyapunov function. Copyright 2009 Rui Zhang et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction This paper is a continuation of Part I 1 . In Section 3 of Part I using the energy estimate and bootstrap arguments the global existence of solutions for a Holling type III cross-diffusion predator-prey model with stage-structure has been discussed when the space dimension be less than 6. However to obtain the L estimate for the population density w of predator species there is not cross-diffusion for w in Part I. All diffusive predator-prey systems behave more or less in the same way for both semilinear and cross-diffusive models at least for small values of the cross diffusivities. Consequently all the available information for linear diffusive models is essential to realize the behavior of the most complicated cross-diffusive systems 2-17 . In this paper we .

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