WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS  

作　　者：黄永忠 郑权 

机构地区：[1]Department of Mathematics Huazhong University of Science and Technology,Wuhan 430074,China [2]School of Mathematics and statistics,Huazhong Normal University,Wuhan 430079,China Department of Mathematics Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Acta Mathematica Scientia》2006年第3期483-490,共8页数学物理学报（B辑英文版）

基　　金：This project was supported by TRAPOYT, the Key Project of Chinese Ministry of Education(104126) the NNSF of China(10371046)

摘　　要：This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.

关 键 词：Ill-posed Cauchy problem QUASI-REVERSIBILITY family of weakly regularizing operators fractional power regularized semigroup 

分 类 号：O177.2[理学—数学]