• Journal of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.715-731
• /
• 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
• /
• v.27 no.4
• /
• pp.463-469
• /
• 1995

The point-kinetics reactor system which is subject to feedback effects may have multiple steady-state solutions for some operating conditions. A necessary and sufficient condition for multiple steady-state solutions of the point-kinetics reactor feedback system for an external input reactivity is obtained through their theoretical approach. If and only if the steady-state feedback reactivity of the reactor system is not strictly monotonic on some values of the feedback variables, then the reactor system has multiple steady-state solutions for the equilibrium operating conditions corresponding to the values of the feedback variables. Also, if and only if the steady--state feedback reactivity is strictly monotonic on all the feedback variables, then the reactor system has only one steady-state solution for all the operating conditions.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.557-569
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.249-281
• /
• 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
• /
• v.26 no.1
• /
• pp.83-92
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.7 no.1
• /
• pp.11-18
• /
• 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
• /
• 2001.10a
• /
• pp.38.6-38
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.4
• /
• pp.445-468
• /
• 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
• /
• v.26 no.2
• /
• pp.99-103
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.11 no.5
• /
• pp.731-739
• /
• 1987

This study has been performed on multiple steady-state natural convection in the upflow region induced by an inclined isothermal plate immersed in pure cold water. The newly found additional steady-state solutions are of considerable practical interest because the heat-transfer rates for a pair of solutions with determining physical parameters and boundary conditions otherwise identical are sometimes vastly different. The results are as follows: First, in the largely upflow region, two solutions exist for 0.15157