• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.527-548
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• 2021

In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.733-763
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• 2006

We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.

• Proceedings of the SAREK Conference
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• 2006.06a
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• pp.132-137
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• 2006

Supercooled type ice slurry system is hard to keep a proper supercooling degree when solution becomes supercooling state. This is the reason of the ice blockage in pipe or cooling part due to an unstable cooling state. In this study, a cooling experiment was performed to pressurized solution in a stationary state. The behaviors during the supercooled aqueous solution were investigated at fixed flow rate of brine and aqueous solution of ethylene glycol 7 mass%. Also the effect to the freezing point of supercooled aqueous solution was investigated to the different pressure 101, 202, 303, and 404 kPa. At results, the pressure of the aqueous solution in the cylinder increased the supercooling degree increased and dissolution of supercooled point decreased.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.819-839
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• 2019

We study the stabilization of 2D g-Navier-Stokes equations in bounded domains with no-slip boundary conditions. First, we stabilize an unstable stationary solution by using finite-dimensional feedback controls, where the designed feedback control scheme is based on the finite number of determining parameters such as determining Fourier modes or volume elements. Second, we stabilize the long-time behavior of solutions to 2D g-Navier-Stokes equations under action of fast oscillating-in-time external forces by showing that in this case there exists a unique time-periodic solution and every solution tends to this periodic solution as time goes to infinity.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.485-490
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• 1998

We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.743-766
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• 2010

We study the existence of weak solution for the stationary Nordstr$\ddot{o}$m-Vlasov equations in a bounded domain. The proof follows by fixed point method. The asymptotic behavior for large light speed is analyzed as well. We justify the convergence towards the stationary Vlasov-Poisson model for stellar dynamics.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1565-1571
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• 2004

Ride characteristics of a vehicle moving on a rough ground with changing travel velocity are analyzed in this paper. The solution is difficult due to the non-stationary characteristics of the problem. Hence a new technique has been proposed to overcome this difficulty. This new technique is employed in the analysis of ride characteristics of a vehicle with changing velocity in the time/frequency domain. It is found that the proposed technique gives successful results in modelling non-stationary responses in terms of a series of stationary responses.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.12
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• pp.850-856
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• 2007

In a supercooled or capsule type ice storage system, aqueous solution (or water) may have trouble with non-uniform dissolution though the system contributes to the simplicity of system and ecological improvement. The non-uniform dissolution increases the instability of the system because it may cause an ice blockage in pipe or cooling part. In order to observe the supercooled state, a cooling experiment was performed with pressurization to an ethylene glycol(EG) 3 mass% solution in stationary state. Also, the effect of the pressurization from 101 to 505 kPa to the dissolution of supercooled aqueous solution was measured with the dissolution time of the supercooled aqueous solution at a fixed cooling rate of brine. At results, the dissolution of supercooled point decreased as the pressure of the aqueous solution in the vessel increased. Moreover, the dissolution point increased as the heat flux for cooling increased.