Global behavior for a diffusive predator-prey system with Holling type II functional response

Yanzhong Zhao

doi:10.1186/1687-2770-2012-111

Abstract

A strongly coupled self- and cross-diffusion predator-prey system with Holling type II functional response is considered. Using the energy estimate, Sobolev embedding theorem and bootstrap arguments, the global existence of non-negative classical solutions to this system in which the space dimension is not more than five is obtained.

Highlights

1 Introduction In this paper, we consider the global existence of non-negative classical solutions to the following diffusion predator-prey system with Holling type II functional response:
We consider the space dimension to be less than six, and initial function u (x) and v (x) under some smooth conditions, using the energy estimate, Sobolev embedding theorem and bootstrap arguments, we consider the global existence of non-negative classical solutions for system ( . )
Authors’ contributions The work was realized by the author

Summary

Introduction

We consider the global existence of non-negative classical solutions to the following diffusion predator-prey system with Holling type II functional response:. We consider the space dimension to be less than six, and initial function u (x) and v (x) under some smooth conditions, using the energy estimate, Sobolev embedding theorem and bootstrap arguments, we consider the global existence of non-negative classical solutions for system – q(q – )α vq– ∇u · ∇v dx + q vq –r + cβmu dx. + amu Integrating the above equation over [ , t] (t ≤ T), it is clear that vq(x, t) dx + (q – )d q q vq (x) dx – q(q – )α vq– ∇u · ∇v dx dt + cβq vq dx dt

It follows from the

When n

Then the condition are satisfied by choosing r

Applying the Schauder estimate know v