대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제19권2호
  • /
  • Pages.293-305
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  • 2004
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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TROTTER-KATO TYPE APPROXIMATIONS OF CONVOLUTED SOLUTION OPERATOR FAMILIES

  • Kim, Mi-Hi (Department of Mathematics Kyung Hee University)
  • 발행 : 2004.04.01
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초록

Trotter-Kato type approximations of the convoluted solution operator families for the Volterra integral equations (V $E_n$): v(t)=$A_{n} \int_0^t v(t-s) d\mu_n(s) + f_n(t), t \geq 0$ and the convergence of the solutions to the equations (V $E_n$) are studied.

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참고문헌

  1. Conf. Semin. Mat. v.259 Laplace transform methods for evolution equations B.Baumer;F.Neubrander
  2. SIAM J. Math. Anal. v.20 Small structured population models and the Trotter-Kato theorem H.J.A.M.Heijmans;J.A.J.Metz https://doi.org/10.1137/0520059
  3. Appl. Anal. v.49 On representations,inversions, and approximations of Laplace transforms in Banach spaces B.Hennig;F.Neubrander https://doi.org/10.1080/00036819108840171
  4. Abstract Volterra equations,Dissertation M.Kim
  5. Commun. Korean Math. Soc. v.12 no.4 Remarks on Volterra equations in Banach spaces
  6. J. Math. Anal. Appl. v.181 On the convergence and approximation of integrated semigroups C.Lizama https://doi.org/10.1006/jmaa.1994.1007
  7. J. Math. Anal. Appl. v.180 The Hille-Yosida and Trotter-Kato theorems for integrated semi groups S.Nicaise https://doi.org/10.1006/jmaa.1993.1402

피인용 문헌

  1. Abstract Volterra equations in locally convex spaces vol.55, pp.9, 2012, https://doi.org/10.1007/s11425-012-4477-9
  2. (a,k)-RegularizedC-Resolvent Families: Regularity and Local Properties vol.2009, 2009, https://doi.org/10.1155/2009/858242