数学物理学报(英文版)

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WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

黄永忠; 郑权   

  1. 华中科技大学数学系, 武汉 430074
  • 收稿日期:2004-08-21 修回日期:1900-01-01 出版日期:2006-07-20 发布日期:2006-07-20
  • 通讯作者: 黄永忠
  • 基金资助:

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

WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

Huang Yongzhong; Zheng Quan   

  1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2004-08-21 Revised:1900-01-01 Online:2006-07-20 Published:2006-07-20
  • Contact: Huang Yongzhong

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-reversibility method and regularized semigroups. Finally, an example is given.

关键词: Ill-posed Cauchy problem, quasi-reversibility, family of weakly regularizingoperators, fractional power, regularized semigroup

Abstract:

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-reversibility method and regularized semigroups. Finally, an example is given.

Key words: Ill-posed Cauchy problem, quasi-reversibility, family of weakly regularizingoperators, fractional power, regularized semigroup

中图分类号: 

  • 47A52