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Properties of Lions's d-semigroups and generalized well-posedness of the Cauchy problem

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References

  1. 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).

    MATH  Google Scholar 

  2. 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.

    Google Scholar 

  3. 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).

    MATH  MathSciNet  Google Scholar 

  4. W. Arendt, “Vector valued Laplace transforms and Cauchy problems,” Israel J. Math.,59, 327–352 (1987).

    MATH  MathSciNet  Google Scholar 

  5. W. Arendt, Sobolev Imbeddings and Integrated Semigroups. Lect. Notes Pure Appl. Math., Vol. 135, Marcel Dekker, New York, 1991.

    Google Scholar 

  6. J. Chazarain, “Problemes de Cauchy abstraits et applications a quelques problems mixtes,” J. Funct. Anal.,7, 386–446 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  7. 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.

    Google Scholar 

  8. 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).

    MATH  MathSciNet  Google Scholar 

  9. H. O. Fattorini, The Cauchy Problem, Addison-Wesley, Reading, Mass., 1983.

    MATH  Google Scholar 

  10. H. Kellerman and M. Hieber, “Integrated semigroups,” J. Funct. Anal.,84, 160–180 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  11. T. Komura, “Semigroups of operators in locally convex spaces,” J. Funct. Anal.,2, 258–296 (1968).

    Article  MATH  MathSciNet  Google Scholar 

  12. R. de Laubenfels, “C-semigroups and the Cauchy problem,” J. Funct. Anal.,111, 44–61 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  13. J.-L. Lions, “Les semi-groupes distributions,” Portug. Math.,19, No. 3–4, 141–161 (1960).

    MATH  Google Scholar 

  14. I. V. Melnikova, “General theory of ill-posed Cauchy problem,” J. Inverse Ill-Posed Probl.,3, No. 2, 149–171 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  15. I. Miyadera, “C-semigroups and semigroups of linear operators,” Semigroup Forum, 133–143 (1990).

  16. F. Neubrander, “Integrated semigroups and their application to the abstract Cauchy problem,” Pacif. J. Math.,135, 111–157 (1988).

    MATH  MathSciNet  Google Scholar 

  17. S. Oharu, “Semigroups of linear operators in a Banach space,” Publ. Res. Inst. Math. Sci.,27, 205–260 (1971).

    MathSciNet  Google Scholar 

  18. M. Sova, “Concerning the characterization of generators of distribution semigroups,” Cas. Pestov. Mat.,105, No. 4, 329–340 (1980).

    MATH  MathSciNet  Google Scholar 

  19. N. Tanaka and N. Okazawa, “LocalC-semigroups and local integrated semigroups,” Proc. London Math. Soc.,61, No. 3, 63–90 (1990).

    MATH  MathSciNet  Google Scholar 

  20. T. Ushijima, “Some properties of regular distribution semigroups,” Proc. Jpn. Acad.,45, 224–227 (1969).

    Article  MATH  MathSciNet  Google Scholar 

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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

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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

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