• 대한수학회지
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• 제49권4호
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• Nuclear Engineering and Technology
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• 제27권4호
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• pp.463-469
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• 1995

궤환효과의 지배를 받는 점동특성시스템은 특정 운전조건에서 여러 개의 정상상태해를 가질 수 있다. 점동특성시스템의 다중해 및 비선형시스템의 일반적인 특성과 관련된 이론적 연구를 통하여, 점동특성시스템이 주어진 외부 입력 반응도에 대해 다중의 정상상태해를 갖기 위한 필요충분조건을 얻었다. 즉 정상상태에서의 궤환반응도가 제환변수의 어떤 값에 대해서 'Strictly Monotoruc'이 아니면, 점동특성시스템은 그 값에 대응되는 운전영역에서 다중의 정상상태해를 갖는다. 반면 정상상태에서의 궤환반응도가 궤환변수의 모든 값에 대해서 'Strictly Monotonic' 이면, 점동특성시스템은 항상 하나의 정상상태해를 갖는다.

• 충청수학회지
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• 제22권3호
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• pp.557-569
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• 2009

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

• 대한수학회지
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• 제57권1호
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• 대한기계학회논문집
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• 제7권1호
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• pp.11-18
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• 1983

For the steady-state solutions of vibratory systems where the dynamics involves nonlinearity and discontinuity, a method of numerical simulation has been normally used. This paper presents a new approach which may overcome some difficulties in the simulation method. This approach is based on the fundamental assumption that the steady-state forced vibration is periodic, so that the problem is formulated as a two-point boundary-value problem and can be solved by Waner's algorithm. This method is demonstrated through the solutions of a linear system, a system with Coulomb friction and an impact pair. It is found that the method gives true solutions well both for linear and nonlinear systems, which convinces us of the usefulness of the method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.38.6-38
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• 2001

This paper presents a steady state optimal control algorithm for the weakly coupled discrete time bilinearsystems. The optimal solution for the overall system is obtained by solving a sequence of reduced order algebraic Riccati equations with an arbitrary accuracy. The obtained solutions converge to the optimal solutions by using the iteration method. We verify the proposed method by applying it to a real world numerical example.

• 충청수학회지
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• 제33권4호
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Journal of Pharmaceutical Investigation
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• 제26권2호
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• pp.99-103
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• 1996

Effects of glycerin and PEG 400 in donor and receptor solutions upon skin permeation of drug were investigated. Deoxycortisone was used as a model compound. In vitro skin permeation study with freshly excised hairless mouse skin was performed and the steady-state skin permeation rates of the drug were determined in different fractions of glycerin or PEG 400 in donor and receptor solutions. Glycerin in donor solution didn't show any effect on the skin permeation rate of deoxycortisone. However glycerin in receptor solution showed significant effect on the skin permeation rate of the drug. In glycerin, there's a critical concentration for balancing hydration and dehydration of skin. At low concentration, less than 20 %, glycerin showed the enhancement of the flux due to the hydration effect of skin. At high concentration, more than 30 %, glycerin retard the permeation rate which might be due to the dehydration effect on the dermis layer. Since dermis has more water content than the stratum corneum, the steady state skin permeation rates were more influenced when glycerin was in receptor solution than that of in donor solution. PEG 400 aqueous solutions doesn't affect the steady state permeation rate of deoxycortisone significantly.

• 대한기계학회논문집
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• 제11권5호
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• pp.731-739
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• 1987

본 연구에서는 K.J.Riu의 연구를 확장하여, 상향유동 영역에서 수직면으로부 터 경사각이 60˚이하인 경사등온면이 저온의 물속에 잠겨있을때 일어나는 다중정상상 태 영역을 밝혀내고, 이 영역에서 경사각이 열전달, 온도분포, 속도분포, 부력분포 및 Nusselt수에 미치는 영향을 구명하였다.또한 해석방법은 이제까지 발표된 연구결과 와 비교검토하기 위하여 기존 논문에서와 같이 상사해석을 사용하였다.