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Volumn 155, Issue 2, 2003, Pages 183-193

On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem

Author keywords

Differential operators; Fractional powers; Incomplete second order abstract Cauchy problem; Operators with polynomially bounded resolvent; Semigroups of growth order

Indexed keywords


EID: 0038036645     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm155-2-7     Document Type: Article
Times cited : (6)

References (19)
  • 2
    • 84972506990 scopus 로고
    • Fractional powers of closed operators and the semigroups generated by them
    • A. V. Balakrishnan, Fractional powers of closed operators and the semigroups generated by them, Pacific J. Math. 10 (1960), 419-437.
    • (1960) Pacific J. Math. , vol.10 , pp. 419-437
    • Balakrishnan, A.V.1
  • 4
    • 0038214368 scopus 로고
    • Existenz und regularität von lösungen semilinearer parabolischer Anfangs-Randwertprobleme
    • H. Kielhöfer, Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme, Math. Z. 142 (1975), 131-160.
    • (1975) Math. Z. , vol.142 , pp. 131-160
    • Kielhöfer, H.1
  • 5
    • 38249009406 scopus 로고
    • Incomplete iterated Cauchy problems
    • R. deLaubenfels, Incomplete iterated Cauchy problems, J. Math. Anal. Appl. 168 (1992), 552-579.
    • (1992) J. Math. Anal. Appl. , vol.168 , pp. 552-579
    • Delaubenfels, R.1
  • 6
    • 0003288365 scopus 로고
    • Existence families, functional calculi and evolution equations
    • Springer, Berlin
    • _, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, Berlin, 1994.
    • (1994) Lecture Notes in Math. , vol.1570
  • 7
    • 0030140663 scopus 로고    scopus 로고
    • Fractional powers of operators of regularized type
    • R. deLaubenfels, F. Yao and S. Wang, Fractional powers of operators of regularized type, J. Math. Anal. Appl. 199 (1996), 910-930.
    • (1996) J. Math. Anal. Appl. , vol.199 , pp. 910-930
    • Delaubenfels, R.1    Yao, F.2    Wang, S.3
  • 9
    • 0037610350 scopus 로고    scopus 로고
    • The theory of fractional powers of operators
    • Elsevier, Amsterdam
    • C. Martínez and M. Sanz, The Theory of Fractional Powers of Operators, North-Holland Math. Stud. 187, Elsevier, Amsterdam, 2001.
    • (2001) North-Holland Math. Stud. , vol.187
    • Martínez, C.1    Sanz, M.2
  • 10
    • 85007909711 scopus 로고
    • Generation theorems of semi-groups of linear operators
    • I. Miyadera, S. Ohary and N. Okazawa, Generation theorems of semi-groups of linear operators, Publ. RIMS Kyoto Univ. 8 (1972/73), 509-555.
    • (1972) Publ. RIMS Kyoto Univ. , vol.8 , pp. 509-555
    • Miyadera, I.1    Ohary, S.2    Okazawa, N.3
  • 11
    • 0012375556 scopus 로고    scopus 로고
    • On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent
    • J. M. A. M. van Neerven and B. Straub, On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent, Houston J. Math. 24 (1998), 137-171.
    • (1998) Houston J. Math. , vol.24 , pp. 137-171
    • Van Neerven, J.M.A.M.1    Straub, B.2
  • 12
    • 0038553232 scopus 로고
    • A generation theorem for semigroups of growth order α
    • N. Okazawa, A generation theorem for semigroups of growth order α, Tôhoku Math. J. 26 (1974), 39-51.
    • (1974) Tôhoku Math. J. , vol.26 , pp. 39-51
    • Okazawa, N.1
  • 13
    • 0037876869 scopus 로고    scopus 로고
    • A functional calculus for almost sectorial operators and applications to abstract evolution equations
    • F. Periago and B. Straub, A functional calculus for almost sectorial operators and applications to abstract evolution equations, J. Evol. Equ. 2 (2002), 41-68.
    • (2002) J. Evol. Equ. , vol.2 , pp. 41-68
    • Periago, F.1    Straub, B.2
  • 14
    • 0038553231 scopus 로고
    • On semigroups of growth α
    • P. E. Sobolevskiǐ, On semigroups of growth α, Soviet Math. Dokl. 12 (1971), 202-205.
    • (1971) Soviet Math. Dokl. , vol.12 , pp. 202-205
    • Sobolevskiǐ, P.E.1
  • 15
    • 84972576787 scopus 로고
    • Fractional powers of operators with polynomially bounded resolvent and the semigroups generated by them
    • B. Straub, Fractional powers of operators with polynomially bounded resolvent and the semigroups generated by them, Hiroshima Math. J. 24 (1994), 529-548.
    • (1994) Hiroshima Math. J. , vol.24 , pp. 529-548
    • Straub, B.1
  • 16
    • 51249176404 scopus 로고
    • Holomorphic C-semigroups and holomorphic semigroups
    • N. Tanaka, Holomorphic C-semigroups and holomorphic semigroups, Semigroup Forum 38 (1989), 253-261.
    • (1989) Semigroup Forum , vol.38 , pp. 253-261
    • Tanaka, N.1
  • 17
    • 0010765572 scopus 로고
    • Gebrochene potenzen eines elliptischen operators und parabolische differentialgleichungen in Räumen hölderstetiger funktionen
    • W. von Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 11 (1972), 231-258.
    • (1972) Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. , vol.11 , pp. 231-258
    • Von Wahl, W.1
  • 18
    • 0038214371 scopus 로고
    • On semigroups with singularities summable with a power-weight at zero
    • A. V. Zafievskiǐ, On semigroups with singularities summable with a power-weight at zero, Soviet Math. Dokl. 11 (1970), 1408-1411.
    • (1970) Soviet Math. Dokl. , vol.11 , pp. 1408-1411
    • Zafievskiǐ, A.V.1
  • 19
    • 0041114396 scopus 로고    scopus 로고
    • Characteristic conditions for the complete infinitesimal generators of analytic semigroups of growth order α
    • X. W. Zhang, Characteristic conditions for the complete infinitesimal generators of analytic semigroups of growth order α, Acta Math. Sci. Ser. B Engl. Ed. 20 (2000), 97-103.
    • (2000) Acta Math. Sci. Ser. B Engl. Ed. , vol.20 , pp. 97-103
    • Zhang, X.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.