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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:230

Article

Wen, Zijuan¹  Fu, Shengmao² 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] NW Normal Univ, Coll Math & Informat Sci, Lanzhou 730070, Peoples R China

关键词: Multi-species;    Cooperating system;    Cross-diffusion;    Global solution;    Stability;   

DOI  :  10.1016/j.cam.2008.10.064

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free