• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.387-401
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• 2006

This paper deals with the problem of a ratio-dependent prey- predator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis. Boundedness of the exploited system is examined. We derive conditions for persistence and global stability of the system. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policy is then solved by using Pontryagin's maximal principle.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.1051-1065
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• 2012

In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.85-97
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• 2009

In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1599-1619
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• 2018

In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity c tends to infinity in a pointwise sense.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1601-1615
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• 2019

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.224-243
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• 2022

In this paper, we prove the global existence of classical solutions to the 2D incompressible Boussinesq equations for the micropolar fluid. Furthermore, applying the Fourier splitting methods, we obtain the lager time decay properties.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.289-292
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• 2008

Recently, several satellite data analyses projects and numerical weather prediction (NWP) reanalysis projects have produced the ocean surface Latent Heat Flux (LHF) data sets in the global coverage. Comparisons of these LHF data sets showed substantial discrepancies in the LHF values. Recently, the increase of LHF in during 1970s-1990s over the global ocean is shown by the LHF data that have been developed at the Objective Analyzed Air-Sea Fluxes (OAFlux) project. It is interesting to investigate the existence of the increase of LHF over a global ocean in the other LHF products. It is interesting to investigate the existence of the increase of LHF over a global ocean in the other LHF products. In this study, we assessed the consistencies and discrepancies of the inter-annual variability and decadal trend for the period 1988-2005 among six LHF products ((J-OFURO2, HOAPS3, IFREMER, NCEP1,2 and OAFlux) over the global ocean. As results, all LHF products showed a positive trend. In particular, the positive trend in satellite-based data analyses (J-OFURO2, HOAPS3, IFREMER) is larger than that in reanalysis products (NCEP1/2). Also, the consistencies and discrepancies are shown on the spatial patterns of the LHF trends across the six data sets. The positive trend of LHF is remarkable in the regions of western boundary currents such as the Kuroshio and the Gulf Stream in all LHF data sets. But, the discrepancies are shown on the spatial patterns of the LHF trends in tropics and subtropics. These discrepancies are primarily caused by the differences of the input meteorological state variables, particularly for the air specific humidity, used to calculate LHF.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.211-224
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• 2018

We consider a certain three dimensional Euler flow with infinite energy, which is sometimes called the columnar or two and half dimensional flow. We prove the global smoothness of such flow in ${\mathbb{R}}^3$ when the initial data is in some Sobolev or Besov spaces and ${\partial}_3u_3$ is nonnegative.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.473-493
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• 2014

This paper concerns with a class of delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.