• 대한수학회지
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• 제43권3호
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• pp.659-676
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• 2006

In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.

• 한국지반신소재학회논문집
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• 제12권1호
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• pp.109-114
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• 2013

본 연구에서는 집중강우에 의해 파괴가 발생한 보강토옹벽의 현장사례를 바탕으로 강우가 보강토옹벽의 안정성 미치는 영향을 분석하기 위하여 침투해석을 수행하였다. 또한 침투해석 결과를 바탕으로 지하수위 변화에 따른 보강토옹벽의 전체사면에 대한 안정성을 평가하였다. 침투해석 결과, 본 연구대상 현장에 형성되는 지하수위는 강우의 영향이 민감하게 작용하는 것으로 확인되었다. 이를 바탕으로 보강토옹벽에 대한 전체사면 안정성을 평가한 결과, 보강토옹벽의 최초 파괴 당시의 안전율이 0.476으로 나타났다. 즉, 보강토옹벽의 전체사면에 대한 활동파괴는 지속적인 강우 및 집중강우로 인하여 과도한 지표수 유입에 따른 급속한 지하수위 상승이 직접적인 원인으로 분석되었다. 따라서 보강토옹벽의 설계 및 시공 시, 최근 발생하고 있는 집중강우를 대비한 설계 및 이를 고려한 다양한 안정해석을 통하여 안정성을 확보할 필요가 있음을 확인하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권2호
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• pp.137-170
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• 2015

In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.

• 대한수학회보
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• 제57권5호
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• pp.1269-1297
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• 2020

In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p₀, where p₀ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.

• 대한수학회지
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• 제55권3호
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• pp.531-551
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• 2018

In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

• 대한수학회논문집
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• 제35권1호
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• pp.321-338
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• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• 대한수학회논문집
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• 제36권3호
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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 Electrical Engineering and Technology
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• 제8권6호
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• pp.1542-1550
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• 2013

This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

• The Journal of Korean Physical Therapy
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• 제16권4호
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• pp.11-22
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• 2004

The concept of segmental stabilization has been one of the most exciting advancements in the field of physical therapy. Specific deep stabilizing muscle have proven to reverse motor control deficits that occurs after back injury. After an injury, a new motor programming strategy is adopted and there is excessive recruitment of the large , strong , global muscular system works instead of small segmental deep muscle recruitment for stability. Many physical therapists and doctors mistakenly prescribe therapeutic exercise for low back pain to use larger, superficial musculature to strengthen the spine for stability and pain control. But motor control coordination of local segmental muscle is actually the key to stability and pain control, not strengthening of global muscle. A recent focus in physiotherapy management of patients with chronic back pain has been the specific training of muscles surrounding the lumbar spine whose primary role is considered to be the provision of dynamic stability and segmental control to the spine. These are the deep transverse abdominis muscle and lumbar multifudus.

• 대한수학회보
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• 제44권3호
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.