关键词: 反应扩散系统; 正稳态解; 非存在性

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