• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.67-73
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• 2008

The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.389-399
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• 1995

We consider the reaction-diffusion system of two-component model in one-dimensional space described by $$ (1) u_s = d_1 u_{xx} + f(u, \upsilon) \upsilon_t = d_2\upsilon_{xx} + \gammag(u, \upsilon) $$ where $d_1$ and $d_2$ are the diffusion rates of u and $\upsilon$, and $\gamma$ is the ration of reaction rates. It is interesting the case of that there are differences in the diffusion and reaction rates of u and $\upsilon$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1597-1612
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• 2016

There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.891-907
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• 2020

In this paper, we consider the Cauchy problem to the tropical climate model. We establish the global regularity for the 2D tropical climate model with generalized nonlocal dissipation of the barotropic mode and obtain a multi-logarithmical vorticity blow-up criterion for the 2D tropical climate model without any dissipation of the barotropic mode.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1521-1537
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• 2021

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in ℝ^d with d ≥ 2, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha [10] who considered the compressible Navier-Stokes equations.

• Nuclear Engineering and Technology
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• v.27 no.1
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• pp.45-52
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• 1995

In influence of the vapor phase turbulent stress (i.e., the too-phase Reynolds stress) to the characteristics of two-phase system in a horizontal pipe has been theoretically investigated. The average two-fluid model has been constituted with closure relations for stratified flow in a horizontal pipe. A vapor phase turbulent stress model for the regular interface geometry has been included. It is found that the second order waves propagate in opposite direction with almost the same speed in the moving frame of reference of the liquid phase velocity. Using the well-posedness limit of the two-phase system, the dispersed-stratified How regime boundary has been modeled. Two-phase Froude number has been found to be a convenient parameter in quantifying the onset of slugging as a function of the global void fraction. The influence of the taper phase turbulent stress was found to stabilize the flow stratification.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.493-506
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• 2000

Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7], They use the well-known fact that the solution of such problem has a singular representation, deduced a well-posed new variational problem for a regular part of solution and an extraction formula for the so-called stress intensity factor using tow cut-off functions. They use Fredholm alternative an Garding's inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for mesh h theoretically. although the numerical experiments shows the convergence for every reasonable h with reasonable size y imposing a restriction to the support of the extra cut-off function without using Garding's inequality. We also give error analysis with similar results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.115-138
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• 2019

The dual singular function method [DSFM] is a solver for corner sigulaity problem. We already construct DSFM in previous reserch to solve the Stokes equations including one singulairity at each reentrant corner, but we find out a crucial incorrection in the proof of well-posedness and regularity of dual singular function. The goal of this paper is to prove accuracy and well-posdness of DSFM for Stokes equations including two singulairities at each corner. We also introduce new applicable algorithms to slove multi-singulrarity problems in a complicated domain.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.81-86
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• 2001

Interfacial pressure jump terms based on the physics of phasic interface and bubble dynamics are introduced into the momentum equations of the two-fluid model for bubbly flow. The pressure discontinuity across the phasic interface due to the surface tension force is expressed as the function of fluid bulk moduli and bubble radius. The consequence is that we obtain from the system of equations the real eigenvalues representing the void-fraction propagation speed and the pressure wave speed in terms of the bubble diameter. Inversely, we obtain an analytic closure relation for the radius of bubbles in the bubbly flow by using the kinematic wave speed given empirically in the literature. It is remarkable to see that the present mechanistic model using this practical bubble radius can indeed represent both the mathematical well-posedness and the physical wave speeds in the bubbly flow.