• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.565-572
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• 2019

In this paper, we consider a Korteweg-de Vries equation in noncylindrical domain. This work is devoted to prove existence and uniqueness of global solutions employing Faedo-Galerkin's approximation and transformation of the noncylindrical domain with moving boundary into cylindrical one. Moreover, we estimate the exponential decay of solutions in the asymptotically cylindrical domain.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.305-334
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• 2005

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1153-1170
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• 2011

In this paper, spatial decay estimates for the time dependent compressible viscous isentropic flow in a semi-infinite three dimensional pipe are derived. An upper bound for the total energy in terms of the initial boundary data is obtained as well. The results established in this paper may be viewed as a version of Saint-Venant's principle in transient compressible Navier-Stokes flow.

• Journal of Ocean Engineering and Technology
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• v.19 no.3
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• pp.25-30
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• 2005

To predict rolling performance for a barge-type FPSO, the evaluation of correct nonlinear roll damping is critical. The square section of FPSO causes a considerable viscous damping effect. Free roll decay tests were carried out to estimate nonlinear roll damping for a barge-type FPSO, under three different conditions. The roll motion RAO was deduced from model tests in the wave condition of the wideband spectrum. In numerical calculation, the quadratic damping was considered as equivalent linear damping, using the results of free roll decay test. Tested roll performance in the JONSWAP wave spectrum was compared with numerical results. These two results shaw good agreement, in spite of the proximity of peak wave period and roll natural period.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1393-1408
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• 2020

In this paper we mainly study existence and regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type with small initial data in Fourier-Besov spaces. To be more detailed, we will explain that global-in-time mild solutions are well-posed and Gevrey regular by means of multilinear singular integrals and Fourier localization argument. Furthermore, we can get time decay rate estimate of mild solutions in Fourier-Besov spaces.

• Journal of the Korean Physical Society
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• v.73 no.11
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• pp.1735-1743
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• 2018

Excitons are the most prominent features of the optical properties of monolayer transition-metal dichalcogenides(TMDC). In view of optoelectronics it is very important to understand the decay mechanisms of the excitons of these materials. Auger recombination of excitons are regarded as one of the dominant decay processes. In this paper the Auger constant of recombination is computed based on the approach proposed by Kavoulakis and Baym. We obtain both temperature dependent (from type A, A' processes) and temperature independent (from type B, B' processes) contributions, and a numerical estimate of theoretical result yields the value of constant in the order of $10^{-2}cm^2s^{-1}$, being consistent with existing experimental data. This implies that Auger decay processes severely limit the photoluminescence yield of TMDC-based optoelectronic devices.

• Bulletin of the Korean Space Science Society
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• 2010.04a
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• pp.29.4-30
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• 2010

A VHF meteor radar at King Sejong Station ($162.22^{\circ}S$, $58.78^{\circ}W$), Antarctica has been observing meteors during a period of March 2007-July 2009. We analyzed the height profiles of the observed meteor decay times between 70 and 95 km by classifying strong and weak meteors according to their estimated electron line densities. The height profiles of monthly averaged decay times show a peak whose altitude varies with season in the range of 80~85 km: higher peak in southern spring and summer than in fall and winter. The higher peak during summer is consistent with colder temperatures that cause faster chemical reactions of electron removal, as effective recombination rates measured by rocket experiments. The height profiles of 15-min averaged decay times show a clear increasing trend with decreasing altitude from 95 km to the peak altitude, especially for weak meteors. This feature for weak meteors is well explained by ambipolar diffusion of meteor trails, allowing one to estimate atmospheric temperatures and pressures, as in previous studies. However, the strong meteors show not only significant scatters but also different slope of the increasing trend from 95 km to the peak altitude. Therefore, atmospheric temperature estimation from meteor decay times should be applied for weak meteors only. In this study, we present the simple model decay times to explain the height profiles of the observed decay times and discuss the additional removal processes of meteor trail electrons through the empirical recombination and by icy particles.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.20 no.2
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• pp.171-183
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• 2022

The parent and daughter nuclides in a radioactive decay chain arrive at secular equilibrium once they have a large half-life difference. The characteristics of this equilibrium state can be used to estimate the production time of nuclear materials. In this study, a mathematical model and algorithm that can be applied to radio-chronometry using the radioactive equilibrium relationship were investigated, reviewed, and implemented. A Bateman equation that can analyze the decay of radioactive materials over time was used for the mathematical model. To obtain a differential-based solution of the Bateman equation, an algebraic numerical solution approach and two different matrix exponential functions (Moral and Levy) were implemented. The obtained result was compared with those of commonly used algorithms, such as the Chebyshev rational approximation method and WISE Uranium. The experimental analysis confirmed the similarity of the results. However, the Moral method led to an increasing calculation uncertainty once there was a branching decay, so this aspect must be improved. The time period corresponding to the production of nuclear materials or nuclear activity can be estimated using the proposed algorithm when uranium or its daughter nuclides are included in the target materials for nuclear forensics.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.487-499
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• 2021

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.1061-1074
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• 2003

We first show the analyticity of Stokes operator in Besov spaces $B_{p,q}$$^{a}$ ( $R_{＋}$$^{n}$). Then, we estimate the asymptotic behavior of the Stokes solutions. We also show the Hodge decomposition.n.