34
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Laplace transform of k-semigroups and well-posedness of cauchy problems

, &
Pages 37-56 | Received 11 Jul 1998, Published online: 03 Apr 2007

References

  • Arendt , W. , El-Mennauoi , O. and Keyantuo , V. 1994 . Local integrated semigroups: evolutions with jumps regularity . J. Math. Anal. and Appl. , 186 ( 2 ) : 572 – 595 .
  • Chazarain , J. 1971 . Problemes de Cauchy abstraits et applications a quelques problemes mixtes . J. Funct. Anal. , 7 ( 3 ) : 386 – 446 .
  • Cioranescu , I. and Lumer , G. 1994 . “ Regularization of evolution equations via kernels K (t), K -evolution operators and convoluted semigroups, generation theorems ” . In Seminar Notes in Func. Anal. and PDEs, 1993-1994 , 45 – 52 . Baton Rouge : Louisianan State Univ. .
  • Cioranescu , I. and Lumer , G. 1995 . On K(t)-convoluted semigroups , Vol. 324 , 86 – 93 . Pitman Research Notes in Mathematics .
  • Cioranescu , I. 168 . “ Local convoluted semigroups ” . In “Evolution Equations”, Lect. notes in pure and appl. math. , 107 – 122 . Marcel Dekker Inc. . (Paper from the Int. Conf. on Evol. Eq., hold at Lousiana State Uni., Jan. 7-11, 1992)
  • Fattorini , H.O. 1983 . The Cauchy problem , Reading, Masse.a. : Addison-Wesley Publ. Co. . (Encycl. Math. and Appl. 18)
  • Ivanov , V.K. and Melnikova , I.V. 1991 . New generalized functions and weak well-posedness of operator problems . Soviet Math. Docl. , 43 ( 2 ) : 315 – 319 .
  • Ivanov , V.K. , Melnikova , I.V. and Filinkov , A.I. 1995 . Differential-operator equations and ill-posed problems , Moscow : Nauka .
  • Komatsu , H. 1973 . Ultradistributions, I. Structure theorems and characterization . J. Fac. Sci., Univ. Tokyo , 20 ( 1 ) : 25 – 106 .
  • Lions , J.-L. 1960 . Les semi-groupes distributions . Portug. math. , 19 ( 3–4 ) : 141 – 161 .
  • Melnikova , I.V. 1997 . Properties of Lions's d-semigroups and generalized well-posedness of the Cauchy problem . Funct. Anal. and Appl. , 31 ( 3 ) : 23 – 34 .
  • Melnikova , I.V. and Alshansky , M.A. 1997 . Well-posedness of the Cauchy problem in a Banach space: regular and degenerate cases . Engl. transl. in J. of Math. Sciences , 87 ( 4 ) : 3732 – 3777 .
  • Melnikova , I.V. 1997 . Well-posedness of differential-operator problems I: the Cauchy problem in spaces of distributions . Itogi nauki i techn. Series sovr. matem. i ee prilog. Analiz / VINITI , 39 ( 4 )
  • Melnikova , I.V. , Anufrieva , U.A. and Ushkov , V.Yu. 1997 . Degenerate distribution semigroups and well-posedness of the Cauchy problem . J. Int. Trans. and Spec. Funct. 6 , 6 ( 1–4 ) : 228 – 237 .
  • Tanaka , N. and Okazawa , N. 1990 . Local C-semigroups and lokal integrated semigroups . Proc. London Math. Soc. , 61 ( 3 ) : 63 – 90 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.