Laplace transform of K-semigroups and well-posedness of Cauchy problems

Integral Transforms and Special Functions

Volumn 9, Issue 1, 2000, Pages 37-56

  Melnikova, I ^a   Anufrieva, U ^a   Filinkov, A ^b  

^a URAL FEDERAL UNIVERSITY   (Russian Federation)

^b NONE

Author keywords

Cauchy problem; Generator; K convoluted semigroup; Resolvent; Ultradistribution; Well posedness

Indexed keywords

EID: 0347303200     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652460008819240     Document Type: Article

References (16)

1. W. Arendt, O. El-Mennauoi and V. Keyantuo, Local integrated semigroups: evolutions with jumps regularity, J. Math. Anal. and Appl. 186 (1994), No.2, 572-595.
2. J. Chazarain, Problemes de Cauchy abstraits et applications a quelques problemes mixtes, J. Funct. Anal. 7 (1971), No.3, 386-446.
3. I. Cioranescu and G. Lumer, Regularization of evolution equations via kernels K(t), K-evolution operators and convoluted semigroups, generation theorems, Seminar Notes in Func. Anal. and PDEs, 1993-1994, Louisiana State Univ., Baton Rouge (1994), 45-52.
4. I. Cioranescu and G. Lumer, On K(t)-convoluted semigroups, Pitman Research Notes in Mathematics 324 (1995), 86-93.
5. I. Cioranescu, Local convoluted semigroups, "Evolution Equations", Lect. notes in pure and appl. math. 168, Marcel Dekker Inc. (1995) (Paper from the Int. Conf. on Evol. Eq., hold at Lousiana State Uni., Jan. 7-11, 1992), 107-122.
6. H.O. Fattorini, The Cauchy problem, Reading, Masse.a.: Addison-Wesley Publ. Co. (1983), (Encycl. Math. and Appl. 18).
7. V.K. Ivanov and I.V. Melnikova, New generalized functions and weak well-posedness of operator problems, Soviet Math. Docl. 43 (1991), No.2, 315-319.
8. V.K. Ivanov, I.V. Melnikova and A.I. Filinkov, Differential-operator equations and ill-posed problems, Moscow, Nauka, 1995.
9. H. Komatsu, Ultradistributions, I. Structure theorems and characterization, J. Fac. Sci., Univ. Tokyo 20 (1973), No.1, 25-106.
10. J.-L. Lions, Les semi-groupes distributions, Portug. math. 19 (1960), No.3-4, 141-161.
11. I.V. Melnikova, Properties of Lions's d-semigroups and generalized well-posedness of the Cauchy problem, Funct. Anal. and Appl. 31 (1997), No.3, 23-34.
12. I.V. Melnikova and M.A. Alshansky, Well-posedness of the Cauchy problem in a Banach space: regular and degenerate cases, Itogi nauki i techn. Series sovr. matem. i ee prilog. Analiz-9 / VINITI, 27 (1995), 5-64; Engl. transl. in J. of Math. Sciences, 87 (1997), No.4, 3732-3777.
13. I.V. Melnikova and M.A. Alshansky, Well-posedness of the Cauchy problem in a Banach space: regular and degenerate cases, Itogi nauki i techn. Series sovr. matem. i ee prilog. Analiz-9 / VINITI, 27 (1995), 5-64; Engl. transl. in J. of Math. Sciences, 87 (1997), No.4, 3732-3777.
14. I.V. Melnikova, 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 (1997).
15. I.V. Melnikova, U.A. Anufrieva and V.Yu. Ushkov, Degenerate distribution semigroups and well-posedness of the Cauchy problem, J. Int. Trans. and Spec. Funct. 6 (1997), No.1-4, 228-237.
16. N. Tanaka and N. Okazawa, Local C-semigroups and lokal integrated semigroups, Proc. London Math. Soc. 61 (1990), No.3, 63-90.