Geodesic
Solvability of the Cauchy Problem for Linear Operator-Differential Equations with Variable Operator Coefficients
Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 672-688.

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We study the Cauchy problem for linear operator-differential equations with unbounded, nondensely defined, variable operator coefficients in a Banach space. We single out new classes of evolution equations of first and second order for which the Cauchy problem is solvable.
Keywords: linear operator-differential equation, Cauchy problem, Banach space, semigroup, Hölder continuity
Mots-clés : evolution equation. 
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M. K. Balaev. Solvability of the Cauchy Problem for Linear Operator-Differential Equations with Variable Operator Coefficients. Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 672-688. http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a3/

[1] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR | Zbl

[2] S. Ya. Yakubov, Lineinye differentsialno-operatornye uravneniya i ikh prilozheniya, Elm, Baku, 1985 | Zbl

[3] P. E. Sobolevskii, “Ob uravneniyakh parabolicheskogo tipa v banakhovom prostranstve”, Tr. MMO, 10, Izd-vo Mosk. un-ta, M., 1961, 297–350 | Zbl

[4] H. Tanabe, “On the equations of evolution in a Banach space”, Osaka Math. J., 12:2 (1960), 363–376 | MR | Zbl

[5] A. Yagi, “Parabolic evolution equations in which the coefficients are generators of infinity differentiable semigroups”, Funkcial. Ekvac., 32:1 (1989), 107–124 ; “Parabolic evolution equations in which the coefficients are generators of infinity differentiable semigroups. II”, Funkcial. Ekvac., 33:1 (1990), 139–150 | MR | Zbl | MR | Zbl

[6] Yu. T. Silchenko, P. E. Sobolevskii, “Razreshimost zadachi Koshi dlya evolyutsionnogo uravneniya v banakhovom prostranstve s neplotno zadannym koeffitsientom, porozhdayuschim polugruppu s osobennostyu”, Sib. matem. zhurn., 27:4 (1986), 93–104 | MR | Zbl

[7] Yu. T. Silchenko, “Evolyutsionnye uravneniya s neplotno zadannym operatornym koeffitsientom”, Sib. matem. zhurn., 34:2 (1993), 166–169 | MR | Zbl

[8] S. Kawatsu, “Cauchy problem for abstract evolution equations of parabolic type”, J. Math. Kyoto Univ., 30:1 (1990), 59–91 | MR | Zbl

[9] Yu. T. Silchenko, “O zadache Koshi dlya lineinogo differentsialnogo uravneniya vtorogo poryadka s peremennymi operatornymi koeffitsientami”, Matem. zametki, 60:1 (1996), 149–152 | MR | Zbl

[10] M. K. Balaev, “Ob evolyutsionnykh uravneniyakh s peremennymi operatornymi koeffitsientami”, Dokl. AN Azerbaidzhana, 55:1-2 (1999), 44–50 | MR

[11] Yu. T. Silchenko, “Ob otsenke rezolventy differentsialnogo operatora vtorogo poryadka s neregulyarnymi granichnymi usloviyami”, Izv. vuzov. Matem., 2000, no. 2, 65–68 | MR | Zbl