• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.749-756
• /
• 2013

In this paper, we consider a diffusive delayed predator-prey model with Beddington-DeAngelis type functional response under homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of immature preys to their maturity. We investigate the global existence of nonnegative solutions and the long-term behavior of the time-dependent solution of the model.

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.395-408
• /
• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1365-1388
• /
• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.379-403
• /
• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.423-443
• /
• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• Proceedings of the KSR Conference
• /
• 2006.11b
• /
• pp.1326-1331
• /
• 2006

The precast concrete deck is one of suitable solutions for replacement and new construction in urban area. However, the precast concrete deck could be a weak point of the steel plate girder bridges structurally due to the connections between precast panels in the longitudinal direction. Thereafter, it is necessary for improvement of durability and load carrying capacity to introduce the prestress force in the longitudinal direction Some cracks of connections at the precast concrete deck may be occurred due to live loads, the difference of temperature and long-term effects. The shrinkage and creep of concrete may significantly affect long-term behaviors which occur tensile stresses at the precast concrete deck of steel plate girder bridges. In this study, the time-dependant analysis program has been developed to determine the initial prestress force in the longitudinal direction considering loss of stress at the precast concrete deck. Also it has been estimated the initial prestress force by construction stages and shapes of girder.

• Structural Engineering and Mechanics
• /
• v.89 no.4
• /
• pp.335-347
• /
• 2024

This study pioneers the exploration of creep and shrinkage behavior in ambient-cured geopolymer concrete (GPC), a vital yet under-researched area in concrete technology. Focusing on the influence of sodium hydroxide (NaOH) solution concentration, the research utilizes low calcium fly ash (Class-F) and alkaline solutions to prepare two sets of GPC. The results show distinct patterns in compressive strength development and dry shrinkage reduction, with a 14 M NaOH solution demonstrating a 26.5% lower dry shrinkage than the 16 M solution. The creep behavior indicated a high initial strain within the first 7 days, significantly influenced by curing conditions and NaOH concentration. This study contributes to the existing knowledge by providing a deeper understanding of the time-dependent properties of GPC, which is crucial for optimizing its performance in structural applications.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.819-839
• /
• 2019

We study the stabilization of 2D g-Navier-Stokes equations in bounded domains with no-slip boundary conditions. First, we stabilize an unstable stationary solution by using finite-dimensional feedback controls, where the designed feedback control scheme is based on the finite number of determining parameters such as determining Fourier modes or volume elements. Second, we stabilize the long-time behavior of solutions to 2D g-Navier-Stokes equations under action of fast oscillating-in-time external forces by showing that in this case there exists a unique time-periodic solution and every solution tends to this periodic solution as time goes to infinity.

• Korea-Australia Rheology Journal
• /
• v.14 no.3
• /
• pp.129-138
• /
• 2002

A cationic surfactant, cetyltrimethylammonium $\rho$-toluenesufonate (CTA$\rho$TS), forms long threadlike micelles in aqueous solution. The threadlike micelles make concentrated entanglement networks, so that the solution shows pronounced viscoelastic behavior as concentrated polymer systems do. However, a mechanism for a process responsible for the longest relaxation time of the threadlike micellar system is different from that of semi-dilute to concentrated polymer systems. The threadlike micellar system exhibits unique viscoelasticity described by a Maxwell model. The longest relaxation time of the threadlike micellar system is not a function of the concentration of CTA$\rho$TS, but changes with that of $\rho$-toluenesufonate ($\rho$$TS^{-}$) ions in the bulk aqueous phase supplied by adding sodium $\rho$-toluenesulfonate (NapTS). The rates of molecular motions in the threadlike micelles are not influenced by the concentration of $\rho$$TS^{-}$ anions, therefore, molecular motions in the threadlike micelles (micro-dynamics) are independent of the longest relaxation mechanism (macro-dynamics). A nonionic surfactant, oleyldimethylamineoxide (ODAO), forms long threadlike micelles in aqueous solution without any additives. The aqueous threadlike micellar system of ODAO also shows Maxwell type viscoelastic behavior. However, the relaxation mechanism for the longest relaxation process in the system should be different from that in the threadlike micellar systems of CTA$\rho$TS, since the system of ODAO does not contain additive anions. Because increase in the average degree of protonation of head groups of ODAO molecules in micelles due to adding hydrogen bromide causes the relaxation time remarkably longer, changes in micro-structure and micro-dynamics in the threadlike micelle are closely related to macro-dynamics in contrast with the threadlike micellar system of CTA$\rho$TS.

• Communications of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.447-463
• /
• 2021

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.