Acta mathematica scientia,Series B

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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

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

CLC Number: 

  • 47A52
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