耗散型双曲系统整体存在性与时间衰减性综述（英文）  

A Survey on Global Existence and Time-decay Estimates for Hyperbolic System With Dissipation

作　　者：徐江[1] 川岛秀一 

机构地区：[1]南京航空航天大学数学系,南京江苏211106 [2]九州大学数学系

出　　处：《数学进展》2017年第3期321-330,共10页Advances in Mathematics（China）

基　　金：The research of Jiang Xu is partially supported by NSFC(No.11471158);the Program for New Century Excellent Talents in University of Ministry of Education(No.NCET-13-0857);the Fundamental Research Funds for the Central Universities(No.NE2015005)

摘　　要：近三十年,基于Littlewood-Paley分解和仿微分演算的傅里叶分析方法在发展型耗散方程的研究中发挥了有效的作用.本文试图给出一个关于耗散型双曲系统整体存在性与时间衰减性工作的综述.基于傅里叶分析的技巧,本文的结果从初值正则性的角度看似乎是最佳的.In recent three decades, Fourier analysis methods based on Littlewood-Paley decomposition and paradifferential calculus have played an efficient role in the study of evolutionary dissipative equations. We here give a survey on the global existence and time-decay results for hyperbolic systems with dissipation. Thanks to Fourier analysis techniques, our results seem to be optimal in the sense of regularity of initial data.

关 键 词：耗散熵 静田-川岛条件 整体存在性 衰减估计式 对称双曲系统 BESOV空间 

分 类 号：O175.27[理学—数学]