Geodesic
Existence of global solutions for a predator-prey model with cross-diffusion
Electronic journal of differential equations, Tome 2008 (2008)
In this article, we prove the existence of global classical solutions for a prey-predator model when the space dimension n10. Under certain conditions on the coefficients of the reaction functions, the convergence of solutions is established for the system with large diffusion by constructing a Lyapunov function.
Classification : 35K57, 35B35, 92D25
Keywords: cross-diffusion, global solution, gradient estimates, stability 
@article{EJDE_2008__2008__a63,
     author = {Xu,  Shenghu},
     title = {Existence of global solutions for a predator-prey model with cross-diffusion},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1138.35349},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a63/}
}
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%J Electronic journal of differential equations
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Xu,  Shenghu. Existence of global solutions for a predator-prey model with cross-diffusion. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a63/