• 제목/요약/키워드: transform semigroup

검색결과 8건 처리시간 0.173초

SEMIGROUP OF LIPSCHITZ OPERATORS

  • Lee, Young S.
    • Korean Journal of Mathematics
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    • 제14권2호
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    • pp.273-280
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    • 2006
  • Lipschitzian semigroup is a semigroup of Lipschitz operators which contains $C_0$ semigroup and nonlinear semigroup. In this paper, we establish the cannonical exponential formula of Lipschitzian semigroup from its Lie generator and the approximation theorem by Laplace transform approach to Lipschitzian semigroup.

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EXPONENTIAL FORMULA FOR C REGULARIZED SEMIGROUPS

  • LEE, YOUNG S.
    • 호남수학학술지
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    • 제26권4호
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    • pp.401-409
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    • 2004
  • In this paper, we show that C-resolvent of generator can be represented by Laplace transform and establish an exponential formula for C regularized semigroups whose antiderivatives are exponentially bounded.

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TROTTER-KATO TYPE CONVERGENCE FOR SEMIGROUPS

  • LEE YOUNG S.
    • Journal of applied mathematics & informatics
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    • 제17권1_2_3호
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    • pp.559-565
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    • 2005
  • In this paper, we establish the convergence of semigroups that are strongly continuous on (0, $\infty$). By using Laplace transform theory, we show some properties of semigroups and the convergence result.

Effect of microtemperatures for micropolar thermoelastic bodies

  • Marin, Marin;Baleanu, Dumitru;Vlase, Sorin
    • Structural Engineering and Mechanics
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    • 제61권3호
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    • pp.381-387
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    • 2017
  • In this paper we investigate the theory of micropolar thermoelastic bodies whose micro-particles possess microtemperatures. We transform the mixed initial boundary value problem into a temporally evolutionary equation on a Hilbert space and after that we prove the existence and uniqueness of the solution. We also approach the study of the continuous dependence of solution upon initial data and loads.

Lp-Boundedness for the Littlewood-Paley g-Function Connected with the Riemann-Liouville Operator

  • Rachdi, Lakhdar Tannech;Amri, Besma;Chettaoui, Chirine
    • Kyungpook Mathematical Journal
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    • 제56권1호
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    • pp.185-220
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    • 2016
  • We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish a principle of maximum for the singular partial differential operator $${\Delta}_{\alpha}={\frac{{\partial}^2}{{\partial}r^2}+{\frac{2{\alpha}+1}{r}{\frac{\partial}{{\partial}r}}+{\frac{{\partial}^2}{{\partial}x^2}}+{\frac{{\partial}^2}{{\partial}t^2}}};\;(r,x,t){\in}]0,+{\infty}[{\times}{\mathbb{R}}{\times}]0,+{\infty}[$$. Later, we define the Littlewood-Paley g-function and using the principle of maximum, we prove that for every $p{\in}]1,+{\infty}[$, there exists a positive constant $C_p$ such that for every $f{\in}L^p(d{\nu}_{\alpha})$, $${\frac{1}{C_p}}{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}{\leqslant}{\parallel}g(f){\parallel}_{p,{\nu}_{\alpha}}{\leqslant}C_p{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}$$.