Singularly Perturbation of the Nonlinear Three Species Prey-predator Reaction Diffusion System
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Abstract:
A class of nonlinear three species in the biomathematics is considered with the prey-predator singularly perturbed problems for the reaction diffusion system method of differential inequalities. Under suitable conditions, the existence and asymptotic behavior of solution for the initial boundary value problems are studied with the theory of differential inequalities. The theory of differential inequalities is really to constructing two auxiliary functions, which are super and lower solutions of the system respectively. And then the super and lower solutions are satisfied corresponding inequalities. Finally, there is a solution of the system between the super solution and lower solution. Then the existence of the solution for the system is proved and the asymptotic estimation is obtained.
