Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics

In this paper, an n -species strongly coupled cooperating diffusive system is considered in a bounded smooth domain, subject to homogeneous Neumann boundary conditions. Employing the method of energy estimates, we obtain some conditions on the diffusion matrix and inter-specific cooperatives to ensu...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 230; no. 1; pp. 34 - 43
Main Authors Wen, Zijuan, Fu, Shengmao
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.08.2009
Elsevier
Subjects
Cooperating system
Cross-diffusion
Exact sciences and technology
Global solution
Mathematical analysis
Mathematics
Multi-species
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Stability
Cross-diffusion
Multi-species
Stability
Cooperating system
Global solution
Numerical analysis
Applied mathematics
Population dynamics
Boundary condition
Steady state
Lotka Volterra model
Numerical stability
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Summary:In this paper, an n -species strongly coupled cooperating diffusive system is considered in a bounded smooth domain, subject to homogeneous Neumann boundary conditions. Employing the method of energy estimates, we obtain some conditions on the diffusion matrix and inter-specific cooperatives to ensure the global existence and uniform boundedness of a nonnegative solution. The globally asymptotical stability of the constant positive steady state is also discussed. As a consequence, all the results hold true for multi-species Lotka–Volterra type competition model and prey–predator model.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.10.064