References
I. V. Melnikova and M. A. Alshansky, “Generalized well-posedness of the Cauchy problem and integrated semigroups,” Russian Math. Dokl.,343, No. 4, 448–451 (1995).
I. V. Melnikova and M. A. Alshansky, “Well-posedness of the Cauchy problem in a Banach space: regular and degenerate cases,” Sovremennaya Matematika i ee Prilozheniya. analiz-9, VINITI,27, 1995, pp. 5–64.
I. V. Melnikova and A. I. Filinkov, “Integrated andC-semigroups. Well-posedness and regularization of differential-operator problems,” Usp. Mat. Nauk,49, No. 6, 111–150 (1994).
W. Arendt, “Vector valued Laplace transforms and Cauchy problems,” Israel J. Math.,59, 327–352 (1987).
W. Arendt, Sobolev Imbeddings and Integrated Semigroups. Lect. Notes Pure Appl. Math., Vol. 135, Marcel Dekker, New York, 1991.
J. Chazarain, “Problemes de Cauchy abstraits et applications a quelques problems mixtes,” J. Funct. Anal.,7, 386–446 (1971).
I. Cioranescu and G. Lumer, “Regularizations of evolution equations via kernelsK(t),K-evolution operators and convoluted semigroups, generation theorems,” LSU Seminar Notes in Funct. Anal. and PDES 1993–1994, Louisiana State Univ., Baton Rouge, 1994, pp. 45–52.
E. B. Davies and M. M. Pang, “The Cauchy problem and a generalization of the Hille-Yosida theorem,” Proc. London Math. Soc.,55, 181–208 (1987).
H. O. Fattorini, The Cauchy Problem, Addison-Wesley, Reading, Mass., 1983.
H. Kellerman and M. Hieber, “Integrated semigroups,” J. Funct. Anal.,84, 160–180 (1989).
T. Komura, “Semigroups of operators in locally convex spaces,” J. Funct. Anal.,2, 258–296 (1968).
R. de Laubenfels, “C-semigroups and the Cauchy problem,” J. Funct. Anal.,111, 44–61 (1993).
J.-L. Lions, “Les semi-groupes distributions,” Portug. Math.,19, No. 3–4, 141–161 (1960).
I. V. Melnikova, “General theory of ill-posed Cauchy problem,” J. Inverse Ill-Posed Probl.,3, No. 2, 149–171 (1995).
I. Miyadera, “C-semigroups and semigroups of linear operators,” Semigroup Forum, 133–143 (1990).
F. Neubrander, “Integrated semigroups and their application to the abstract Cauchy problem,” Pacif. J. Math.,135, 111–157 (1988).
S. Oharu, “Semigroups of linear operators in a Banach space,” Publ. Res. Inst. Math. Sci.,27, 205–260 (1971).
M. Sova, “Concerning the characterization of generators of distribution semigroups,” Cas. Pestov. Mat.,105, No. 4, 329–340 (1980).
N. Tanaka and N. Okazawa, “LocalC-semigroups and local integrated semigroups,” Proc. London Math. Soc.,61, No. 3, 63–90 (1990).
T. Ushijima, “Some properties of regular distribution semigroups,” Proc. Jpn. Acad.,45, 224–227 (1969).
Additional information
This paper is partially supported by RFBR grant No. 95-01-00283.
Ural State University, Department of Mathematics and Mechanics. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 31, No. 3, pp. 23–34, July–September, 1997.
Translated by I. V. Melnikova
Rights and permissions
About this article
Cite this article
Melnikova, I.V. Properties of Lions's d-semigroups and generalized well-posedness of the Cauchy problem. Funct Anal Its Appl 31, 167–175 (1997). https://doi.org/10.1007/BF02465784
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02465784