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An identification problem for a linear evolution equation in a Banach space and applications
1.  Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano 
2.  "O. Mayer" Mathematics Institute of the Romanian Academy, Iaşi 700505, Romania 
References:
[1] 
Yu. Anikonov and A. Lorenzi, Explicit representation for the solution to a parabolic differential identification problem in a Banach space, J. Inverse Ill Posed Problems, 15 (2007), 669683. Google Scholar 
[2] 
J. Diestel and J. J. Uhl, Jr., "Vector Measures," Mathematical Surveys, 15, American Mathematical Society, 1977. Google Scholar 
[3] 
I. Dobrakov, On integration in Banach spaces. I, Czechoslovak Math. J., 20 (1970), 511536. Google Scholar 
[4] 
I. Dobrakov, On integration in Banach spaces. II, Czechoslovak Math. J., 20 (1970), 680695. Google Scholar 
[5] 
A. I. Prilepko and A. B. Kostin, An estimate for the spectral radius of an operator and the solvability of inverse problems for evolution equations, Mat. Zametki, 53 (1993), 8994. Google Scholar 
[6] 
A. I. Prilepko and I. V. Tikhonov, Reconstruction of the inhomogeneous term in an abstract evolution equation, Izv. Ross. Akad. Nauk Ser. Mat., 58 (1994), 167188. Google Scholar 
[7] 
A. I. Prilepko, S. Piskarev and S.Y. Shaw, On approximation of inverse problem for abstract parabolic differential equation in Banach spaces, J. Inv. IllPosed Problems, 15 (2007), 831851. Google Scholar 
[8] 
I. V. Tikhonov and Yu. S. Eidel'man, Problem of correctness of ordinary and inverse problems for evolutionary equations in special form, Mat. Zametki, 56 (1994), 99113. (Russian) (English Translation: Mathematical Notes, pp. 830839). Google Scholar 
[9] 
I. V. Tikhonov and Yu. S. Eidel'man, The unique solvability of a twopoint inverse problem for an abstract differential equation with unknown parameter, Differential'nye Uravneniya, 36 (2000), 11321133. Google Scholar 
[10] 
I. V. Tikhonov and Yu. S. Eidel'man, Theorems of the mapping point spectrum for $C_0$semigroups and their application to uniqueness problems for abstract differential equations, Dokl. Akad. Nauk, 394 (2004), 3235. Google Scholar 
[11] 
I. Vrabie, "Compactness Methods for Nolinear Evolutions. Second Edition," Pitman Monographs and Surveys in Pure and Applied Mathematics, 75, Longman Scientific & Technical, Harlow; John Wiley & Sons Inc., New York, 1995. Google Scholar 
[12] 
I. I. Vrabie, "$C_0$Semigroups and Applications," NorthHolland Publishing Co. Amsterdam, 2003. Google Scholar 
show all references
References:
[1] 
Yu. Anikonov and A. Lorenzi, Explicit representation for the solution to a parabolic differential identification problem in a Banach space, J. Inverse Ill Posed Problems, 15 (2007), 669683. Google Scholar 
[2] 
J. Diestel and J. J. Uhl, Jr., "Vector Measures," Mathematical Surveys, 15, American Mathematical Society, 1977. Google Scholar 
[3] 
I. Dobrakov, On integration in Banach spaces. I, Czechoslovak Math. J., 20 (1970), 511536. Google Scholar 
[4] 
I. Dobrakov, On integration in Banach spaces. II, Czechoslovak Math. J., 20 (1970), 680695. Google Scholar 
[5] 
A. I. Prilepko and A. B. Kostin, An estimate for the spectral radius of an operator and the solvability of inverse problems for evolution equations, Mat. Zametki, 53 (1993), 8994. Google Scholar 
[6] 
A. I. Prilepko and I. V. Tikhonov, Reconstruction of the inhomogeneous term in an abstract evolution equation, Izv. Ross. Akad. Nauk Ser. Mat., 58 (1994), 167188. Google Scholar 
[7] 
A. I. Prilepko, S. Piskarev and S.Y. Shaw, On approximation of inverse problem for abstract parabolic differential equation in Banach spaces, J. Inv. IllPosed Problems, 15 (2007), 831851. Google Scholar 
[8] 
I. V. Tikhonov and Yu. S. Eidel'man, Problem of correctness of ordinary and inverse problems for evolutionary equations in special form, Mat. Zametki, 56 (1994), 99113. (Russian) (English Translation: Mathematical Notes, pp. 830839). Google Scholar 
[9] 
I. V. Tikhonov and Yu. S. Eidel'man, The unique solvability of a twopoint inverse problem for an abstract differential equation with unknown parameter, Differential'nye Uravneniya, 36 (2000), 11321133. Google Scholar 
[10] 
I. V. Tikhonov and Yu. S. Eidel'man, Theorems of the mapping point spectrum for $C_0$semigroups and their application to uniqueness problems for abstract differential equations, Dokl. Akad. Nauk, 394 (2004), 3235. Google Scholar 
[11] 
I. Vrabie, "Compactness Methods for Nolinear Evolutions. Second Edition," Pitman Monographs and Surveys in Pure and Applied Mathematics, 75, Longman Scientific & Technical, Harlow; John Wiley & Sons Inc., New York, 1995. Google Scholar 
[12] 
I. I. Vrabie, "$C_0$Semigroups and Applications," NorthHolland Publishing Co. Amsterdam, 2003. Google Scholar 
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