一类反应扩散系统非常数正解的非存在性

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

考虑了一类齐次Neumann边界条件下具反馈效应的反应扩散系统的平衡态,建立了正稳态解的先验估计。运用能量方法和隐函数定理分析扩散系数对非常数正稳态解的非存在性的影响。结果表明,当三个扩散系数之任一足够大时,该反应扩散系统的平衡态不存在非常数正解。

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 so- lutions are analyzed by the energy method and implicit functional theorem. The results show that if one of the coeffi- cients is large enough, the system has no positive non-constant steady-state solutions.