Weak regularization for a class of ill-posed Cauchy problems

作者：Huang Yongzhong^*; Zheng Quan

来源：Acta Mathematica Scientia, 2006, 26(3): 483-490.

DOI：10.1016/S0252-9602(06)60073-8

• ill-posed Cauchy problem
• quasi-reversibility
• family of weakly regularizing operators
• fractional power
• regularized semigroup

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.

• 出版日期2006-7
• 单位华中师范大学