Uniform boundedness and stability of global solutions in a strongly coupled three-species cooperating model

Using the energy estimate and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for a strongly coupled reaction-diffusion system are proved. This system is the Shigesada-Kawasaki-Teramoto three-species cooperating model with self- and cross-population pressure. Meanwhile, some criteria on the global asymptotic stability of the positive equilibrium point for the model are also given by Lyapunov function. As a by-product, we proved that only constant steady states exist if the diffusion coefficients are large enough. (c) 2006 Elsevier Ltd. All rights reserved.