Regularization for a class of ill-posed Cauchy problems

Huang, Yongzhong; Zheng, Quan

doi:10.1090/S0002-9939-05-07822-6

Regularization for a class of ill-posed Cauchy problems
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by Yongzhong Huang and Quan Zheng PDF

Proc. Amer. Math. Soc. 133 (2005), 3005-3012 Request permission

Abstract:

This paper is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator $A$ in a Banach space. Our main result is that if $-A$ is the generator of an analytic semigroup of angle $\ge \pi /4$, then there exists a family of regularizing operators for such an ill-posed Cauchy problem by using the Gajewski and Zacharias quasi-reversibility method, and semigroups of linear operators.

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