• Korean Journal of Mathematics
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• v.14 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.141-157
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• 2015

The purpose of this paper is first of all to investigate the behavior of admixable operators on the product of abstract Wiener spaces and secondly to examine transform semigroups which consist of admix-Wiener transforms on abstract Wiener spaces.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.165-169
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• 2004

In this paper, we establish an inversion formula for exponentially bounded C-regularized semigroup.

• Honam Mathematical Journal
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• v.26 no.4
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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.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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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.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.349-354
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• 2014

In this paper, we establish convergence of contraction $C_0$ semigroups in the weak topology on a general Banach space. We remove the restriction on a Banach space X and weaken the condition on resolvents of generators in the previous results [4, 5].

• Structural Engineering and Mechanics
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• v.61 no.3
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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.

• Kyungpook Mathematical Journal
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• v.56 no.1
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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 $f{\in}L^p(d{\nu}_{\alpha})$, $${\frac{1}{C_p}}{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}{\leqslant}{\parallel}g(f){\parallel}_{p,{\nu}_{\alpha}}{\leqslant}C_p{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}$$.