圆周上时间周期反应扩散方程全局吸引子的存在条件

An Existence Condition for Global Attractor of Time-Periodic Reaction-Diffusion Equations on the Circle

针对圆周上时间周期反应扩散方程,给出耗散性假设,证明了该方程存在全局吸引子.首先,建立合适的分数幂空间,应用算子半群的相关理论证明该方程在此分数幂空间中存在全局解.其次,基于全局解定义Poincaré映射,生成离散半流.最终由离散半流的紧性和点耗散性得到全局吸引子的存在性.

For a time-periodic reaction-diffusion equation on the circle,the existence of a global attractor was proved under dissipative assumptions.Firstly,a suitable fractional power space was established in this paper,and by using the operator semigroup theory it can be proved that the equation has a global solution in the space.Next,based on the global solution,the Poincarémap was defined,which can generate a discrete semiflow.Finally,the existence of the global attractor was obtained from the compactness and point dissipativity of the discrete semiflow.