THE　UNIQUENESS　AND　CONTINUOUS　DEPENDENCE　FOR　CHARACTERISTIC　CAUCHY　PROBLEM　OF　PARTIAL　DIFFERENTIAL　EQUATIONS

作     者：栾文贵 刘伟霞 

作者机构：Computing Center Academia Sinica Beijing China Beijing Information Technology Institute Beijing 100101 China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：1995年第15卷第4期

页      面：442-457页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：国家自然科学基金 

主　　题：Pseudo-differential operators Factorization Estimation. 

摘      要：in this paper, we investigate the connection between the uniqueness and the continuous dependence for the Cauchy problem of linear partial differential equations with everywhere characteristic initial hypersurface. The local Carleman s estimate used by S. Alinhac and M. S. Baouendi to prove the uniqueness for the characteristic Cauchy problem is improved to the global estimate with a specific peaking weight factor. Using this estimate, we can prove similarly the uniqueness of the characteristic Cauchy problem. In particular, we derive also the continuous dependence for the solution of this problem in the function class that a certain norm is bounded by the aid of the same inference of proving the global estimate.