• Title/Summary/Keyword: smallness condition

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EXPONENTIAL DECAY FOR THE SOLUTION OF THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH MEMORY CONDITION AT THE BOUNDARY

  • Kim, Daewook
    • East Asian mathematical journal
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    • v.34 no.1
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    • pp.69-84
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    • 2018
  • In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE

  • Kim, Daewook
    • East Asian mathematical journal
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    • v.32 no.1
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    • pp.117-128
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    • 2016
  • In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM

  • Kim, Daewook
    • East Asian mathematical journal
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    • v.32 no.3
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    • pp.399-412
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    • 2016
  • In this paper, we study the viscoelastic Kirchhoff type equation with the following nonlinear source and time-varying delay $$u_{tt}-M(x,t,{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\int_{0}^{t}}h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\+{\parallel}u{\parallel}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY

  • Kim, Daewook
    • East Asian mathematical journal
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    • v.32 no.5
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    • pp.659-675
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    • 2016
  • In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history $$\large u_{tt}-M(x,t,{\tau},\;{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\\hspace{25}-{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{-{\infty}}}^t}\;k(t-{\tau}){\Delta}u(x,t)d{\tau}+{\mid}u{\mid}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

Sloshing Flow of Highly-Viscous Fluid in a Rectangular Box (사각용기에서 발생하는 고점성 유체의 슬로싱 유동)

  • park, Jun Sang
    • Journal of the Korean Society of Visualization
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    • v.17 no.3
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    • pp.39-45
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    • 2019
  • A study on the sloshing flow of highly-viscous fluid in a rectangular box was made by both of theoretical approach and experimental visualization method. Assuming a smallness of external forcing to oscillate the container, it was investigated a linear sloshing flow of highly-viscous fluid utilizing asymptotic analysis by Taylor-series expansion as a small parameter Re (≪1) in which Re denotes Reynolds number. The theory predict that, during all cycles of sloshing, a linear shape of free surface will prevail in a bulk zone and it has confirmed in experiment. The relevance of perfect slip boundary condition, adopted in theoretical approach, to the bulk zone flow at the container wall was tested in experiment. It is found that quasi-steady coated thin film, which makes a lubricant layer between bulk flow and solid wall, is generated on the wall and the film makes a role to perfect slip boundary condition.

A Study on Experiment and Structural Analysis for High-Durability of Orthotropic Steel Deck Bridge (고내구성을 위한 강바닥판교의 실험 및 해석 연구)

  • Kong, Byung-Seung;Kim, Min-Ho
    • Proceedings of the KSR Conference
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    • 2007.11a
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    • pp.462-467
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    • 2007
  • From the research which it sees verification of the whole interpretation and local interpretation of the durability steel deck bridge a static test and it produces the test body which it sells with character and it executes smallness pul lek detailed interpretation it leads and the appropriate characteristic of smallness pul lek detailed interpretation and to sleep a nominal stress price and it compares it judges it does. The stress quality from each structure region which it follows in load stock location it analyzes and from the hazard which evaluates, the objective region the length rib and the bottom grater weld zone, the length rib and width rib connection department and the width rib with the father it divided. It investigated the stress distribution of the test body from these objective location, FEM interpretation it led and the conduct against each structure state tax it analyzed. General conduct the load stock location the floor plate is located in the center with interpretation price together symmetry characteristic to seem, it cannot be like that it cannot there is one actual test price. Like this reason the length rib and width rib connection actually production even production characteristic security it is a day when it is impossible with the curvature junction department which it blows, it follows in examination body deferment condition and form feed with the fact that it is visible a big difference even with error of some it becomes. Consequently for a data and the research which are more accurate it is judged with the fact that the effort which is prudent will be necessary.

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A study on Supply Extension Device of AED (AED의 보급 확대 방안에 관한 연구)

  • Koh, Jae-Moon;Kim, Young-Ho;Han, Sang-Hak
    • The Korean Journal of Emergency Medical Services
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    • v.9 no.2
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    • pp.147-168
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    • 2005
  • It examined the doubt point which AED motive relates until now, the AED should have bought a life how, present address of our country site pre-hospital care, comparison it tried to observe the advanced nation instance back. Gist of this research the AED important cold region once compared to informed to how many cardiac arrest patient, against him the what kind of preparation wanted informing the necessary cold region. It soaks simultaneously but the AED motive is widely supplied distant in future and it is generality and it is feeble but it wanted doing one morning. The habit difference of an American who does of course meat diet mainly and a Korean is many and it compares in the United States and the cardiac arrest patient comparison occurs holds a point few. To become Western anger but and be caused by with thin dietary life, stanching bleeding cung, with the fact that the heart attack is increasing rapidly with the hyperextension. It is a talk which anyone it knows all. The major league most Choi huy Sub in condition will catch the ball which floats and the multi co-player and to collide when falling down, the medical device which is committed with emergency aid is AED motive. From the United States subway station and the shopping which are a public place on the baseball field outside the jar which it will drive, the museum and the school, easily there is it will be able to discover the AED from the court of justice back. The Pittsburg university the students per the individual $30 the core phyey were receiving the smallness lifestyle alcoholic beverage and a AED motive actual training with mercy of degree. From the United States distant in future the AED motive is sold even from the retail store and. From our country like this plan government offices temporary disposal education from from 119 fire fighters emergency structure company in fire fighting government employee and nursing must magnify a former enterprise rainy spell in summer multi temporary disposal education with the head which it will burn with the head. This plan in early rising will be able to become fixed in Korea it forecasts with the fact that. The research which it sees it leads and like the United States to some day become fixed even from our country to believe and suspicion it is not and in the people in approach ease one AED supply plan fire fighting government employees stand in the first and feed with the fact that must be positive at this enterprise they become.

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