Uniform boundedness and stability of global solutions in a strongly coupled three-species cooperating model |
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Institution: | 1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, PR China;2. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, PR China |
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Abstract: | 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. |
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