J4 ›› 2010, Vol. 45 ›› Issue (11): 88-92.

• Articles • Previous Articles     Next Articles

Non-existence of positive non-constant steady-states of a certain class of reaction-diffusion systems

BIE Qun-yi   

  1. College of Science, China Three Gorges University, Yichang 443002, Hubei, China
  • Received:2009-07-20 Online:2010-11-16 Published:2010-11-24

Abstract:

 A certain class of reaction-diffusion systems with feedback effect subject to homogeneous Neumann boundary condition and the positive steady-state solutions are considered. Some priori estimates are established for positive steady-state solutions, then the effects of the diffusion coefficient on the nonexistence of positive non-constant steady-state solutions are analyzed by the energy method and implicit functional theorem. The results show that if one of the coefficients is large enough, the system has no positive non-constant steady-state solutions.

Key words: reaction-diffusion system; positive steady-state solutions; non-existence

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