摘要
研究高阶Allen-Cahn系统的吸引子的正则性.首先,利用线性算子的正则性估计证明Allen-Cahn系统的解在H^(γ)(γ≥0)空间中有界;然后,通过迭代方法得到方程在H^(γ)(γ≥0)空间中存在有界的吸收集.进而根据分数次空间吸引子存在性定理得到在H^(γ)(γ≥0)空间中全局吸引子的存在性.
In this paper,the regularity of global attractors for higher-order Allen-Cahn system is investigated.Firstly,it is proved that the solution of higher-order Allen-Cahn system is bounded in H^(γ)(γ≥0)spaces through regularity estimates for the linear semigroups.Secondly,the bounded absorbing set of the system is presented in H^(γ)(γ≥0)spaces by using iteration procedures.Finally,it is shown that the higher-order Allen-Cahn system possesses a global attractor in H^(γ)spaces forγ≥0 from existence theorem of global attractor in fractional order spaces.
作者
潘娇娇
罗宏
PAN Jiaojiao;LUO Hong(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)
出处
《四川师范大学学报（自然科学版）》
CAS
2021年第3期323-328,共6页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(11701399)。
关键词
全局吸引子
正则性
算子半群
插值不等式
global attractors
regularity
semigroup of operator
interpolation inequality
