Acta mathematica scientia,Series B
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Huang Yongzhong; Zheng Quan
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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
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Huang Yongzhong; Zheng Quan. WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS[J].Acta mathematica scientia,Series B, 2006, 26(3): 483-490.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(06)60073-8
http://121.43.60.238/sxwlxbB/EN/Y2006/V26/I3/483
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