Properties of an abstract pseudoresolvent and well-posedness of the degenerate Cauchy problem

• Autorzy: Irina V. Melnikova
• Języki publikacji: EN

Abstrakty

EN

The degenerate Cauchy problem in a Banach space is studied on the basis of properties of an abstract analytical function, satisfying the Hilbert identity, and a related pair of operators A, B.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 151-157

Daty

wydano

1996

Twórcy

autor

Irina V. Melnikova

• Department of Mathematics, Ural State University, Pr. Lenina 51, 620083 Ekaterinburg, Russia

Bibliografia

• [1] K. Yosida, Functional Analysis, Springer-Verlag, Berlin and New York, 1980.
• [2] W. Arendt, Vector valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 59 pp.
• [3] S. G. Krein, Linear differential equations in a Banach space, Amer. Math. Soc., Providence, R.I., 1972.
• [4] V. K. Ivanov, I. V. Melnikova, and A. I. Filinkov, Differential-operator equations and ill-posed problems, Nauka, Moscow, 1994 [in Russian].
• [5] N. Tanaka and I. Miyadera, Exponentially bounded C-semigroups and integrated semigroups, Tokyo J. Math. 12, no. 1 (1989), 99-115.
• [6] I. V. Melnikova and M.A. Alshansky, Well-posedness of the Cauchy problem in a Banach space: regular and degenerate cases, J. Math. Sci., Plenum, 1994, to appear.
• [7] E. B. Davies and M. M. Pang, The Cauchy problem and a generalizations of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987), 181-208.
• [8] I. V. Melnikova and S.V. Bochkareva, C-semigroups and regularization of an ill-posed Cauchy problem, Russia Acad. Sci. Docl. Math. 47, no. 2 (1993), 228-232.