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Existence of the solutions of a reaction cross-diffusion model for two species |
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| Institution: | Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, College of Mathematics and Computers, Gannan Normal University, Ganzhou, Jiangxi 341000, PR China;Department of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, Guangdong 519082, PR China |
| Abstract: | In this paper, we investigate a two-cooperative species model with reaction cross-diffusion under the Dirichlet boundary value condition. By applying Lyapunov–Schmidt reduction method and some important formulas, we obtain the existence of coexistence solutions under some given conditions. |
| Keywords: | Cooperative species Cross-diffusion Semi-trivial steady state Coexistence solution Lyapunov–Schmidt reduction |
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