带粘性含不活泼项的Cahn-Hilliard方程解的逐点估计  

Pointwise Estimates of Solutions for the Viscous Cahn-Hilliard Equation with Inertial Term

作　　者：王一平 徐红梅[1] Wang Yiping;Xu Hongmei(School of science, Hohai University, Nanjing 210098, China)

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《海南大学学报（自然科学版）》2020年第1期1-5,共5页Natural Science Journal of Hainan University

基　　金：国家自然科学基金(11571092)。

摘　　要：研究了高维空间带粘性含不活泼项的Cahn-Hilliard方程解的逐点估计.首先结合格林函数,频谱分解等工具进行详细分析,然后利用不动点原理得到了方程经典解的存在性,最后在此基础上,进一步得到方程解在任意时刻和空间任意点处的衰减估计.In the report,the pointwise estimates of the solutions for the viscous Cahn-Hilliard equation with inertial term in high-dimensional space were studied.At first,the detailed analysis of the Green’s function,spectrum decomposition and other tools were performed;secondly,the fixed point principle was used to obtain the existence of the classical solution;lastly,on which the decay estimates of solutions for the equation at any time and at any point in space were obtained.

关 键 词：带粘性含不活泼项的Cahn-Hilliard方程 柯西问题 逐点估计 格林函数 

分 类 号：O175.28[理学—数学]