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

✍ Scribed by Zijuan Wen; Shengmao Fu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 628 KB
• Volume: 230
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.10.064

✦ Synopsis

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 multispecies Lotka-Volterra type competition model and prey-predator model.