• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.465-477
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• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1440-1448
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• 2004

Multiple solutions in natural convection of air (Pr=0.7) between two horizontal walls with mean temperature difference and the same periodic nob-uniformities are investigated. An analytical solution is found for small Rayleigh number, and the general solution is investigated by using a numerical method. In the conduction-dominated regime, two upright cells are formed between two walls over one wave length. When the wave number is small, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximately square-shape cells. And several kinds of multiple flows classified by the number of cells are found.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.873-894
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• 2021

In this paper, we consider the Gudnason model of 𝒩 = 2 supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.225-247
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• 2010

In this paper, we establish a two-competitive-prey and one-predator Holling type II system by introducing a proportional periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for the predator at different fixed time. We show the boundedness of the system and find conditions for the local and global stabilities of two-prey-free periodic solutions by using Floquet theory for the impulsive differential equation, small amplitude perturbation skills and comparison techniques. Also, we prove that the system is permanent under some conditions and give sufficient conditions under which one of the two preys is extinct and the remaining two species are permanent. In addition, we take account of the system with seasonality as a periodic forcing term in the intrinsic growth rate of prey population and then find conditions for the stability of the two-prey-free periodic solutions and for the permanence of this system. We discuss the complex dynamical aspects of these systems via bifurcation diagrams.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.47-54
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• 2007

A periodic CFD approach for the performance analysis of compact high temperature heat exchangers is introduced and applied to selected benchmark problems, which are a fully developed 2D laminar heat transfer, a conjugate heat transfer between parallel plates which have exact solutions, and a heat transfer in a real high temperature heat exchanger module. The results for the 2D laminar heat transfer and the 2D conjugate heat transfer showed a very good agreement with the exact solutions. For the high temperature heat exchanger module, the pressure drops were predicted well but some difference was observed in the temperature parameters when compared to the full channel CFD analysis due to assumptions introduced into the periodic approach. Considering its assumptions and simplicities, however, the results showed that the periodic approach provides physically reasonable results and it is sufficient to predict the performance of a heat exchanger within an engineering margin and with much less CPU time than the case of a full channel analysis.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.697-710
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• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.99-112
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• 2015

In this paper we consider the periodic Cauchy problem for the generalized two-component Hunter-Saxton system with analytic initial data and we prove a Cauchy-Kowalevski type theorem for the generalized two-component Hunter-Saxton system, that establishes the existence and uniqueness of real analytic solutions.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.1-11
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• 2018

We use Krasnoselskii's fixed point theorem to show that the neutral differential equation $$\frac{d}{dt}[x(t)-a(t)x(\tau(t))]+p(t)x(t)+q(t)x(\tau(t))=0,\;t{\geq}t_0$$, has a positive periodic solution. Some examples are also given to illustrate our results. The results obtained here extend the work of Olach [13].

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.287-300
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• 2003

In this paper we shall consider the nonlinear delay differential equation (equation omitted) where m is a positive integer, ${\beta}$(t) and $\delta$(t) are positive periodic functions of period $\omega$. In the nondelay case we shall show that (*) has a unique positive periodic solution (equation omitted), and show that (equation omitted) is a global attractor all other positive solutions. In the delay case we shall present sufficient conditions for the oscillation of all positive solutions of (*) about (equation omitted), and establish sufficient conditions for the global attractivity of (equation omitted). Our results extend and improve the well known results in the autonomous case.