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

作者：Fu, Shengmao; Wen, Zijuan^*; Cui, Shangbin

来源：Nonlinear Analysis: Real World Applications , 2008, 9(2): 272-289.

DOI：10.1016/j.nonrwa.2006.10.003

• self-diffusion
• cross-diffusion
• global solutions
• uniform boundedness
• stability

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.

• 出版日期2008-4
• 单位西北师范大学; 中山大学