• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.1-28
• /
• 2021

We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to zero.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1921-1930
• /
• 2018

We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.321-338
• /
• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.05a
• /
• pp.31-36
• /
• 2003

Using a short time expansion of the fundamental solution of heat equation by analysis of Wiener functional with the help of Malliavin calculus, we obtain the asymptotic expansion of the mean distance of Brownian motion on Riemannian manifolds.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.229-234
• /
• 2005

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}},\;\; n = 0, 1, ...$ is investigated, where all the coefficients are nonnegative real numbers.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.797-804
• /
• 2010

The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.15-26
• /
• 2002

In this paper, we suggest and analyze a class of resolvent dynamical systems associated with mixed variational inequalities. We study the globally asymptotic stability of the solution of the resolvent dynamical systems for the pseudomonotone operators. We also discuss some special cases, which can be obtained from our main results.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.561-568
• /
• 2011

We investigate the stability property and existence of almost periodic solutions of discrete Volterra equations with unbounded delay.

• Structural Engineering and Mechanics
• /
• v.43 no.3
• /
• pp.311-320
• /
• 2012

The higher-order asymptotic C(t) - $A_2(t)$ approach was employed to investigate the crack-tip stress of two collinear cracks in a power-law creeping material under the plane strain conditions. A comprehensive calculation was made of the single crack, collinear crack model with S/a = 0.4 and 0.8, by using the C(t) - $A_2(t)$ approach, HRR-type field and the finite element analysis; the latter two methods were used to check the constraint significance and the calculation accuracy of the C(t) - $A_2(t)$ approach, respectively. With increasing the creep time, the constraint $A_2$ was exponentially increased in the small-scale creep stage, while no discernible dependency of the constraint $A_2$ on the creep time was found at the extensive creep state. In addition, the creep time and the mechanical loads have no distinct influence on accuracy of the results obtained from the higher-order asymptotic C(t) - $A_2(t)$ approach. In comparison with the HRR-type field, the higher-order asymptotic C(t) - $A_2(t)$ solution matches well with the finite element results for the collinear crack model.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.13 no.1
• /
• pp.50-56
• /
• 2021

An accurate evaluation of three-dimensional (3D) Time-Domain Green Function (TDGF) in infinite water depth is essential for ship's hydrodynamic analysis. Various numerical algorithms based on the TDGF properties are considered, including the ascending series expansion at small time parameter, the asymptotic expansion at large time parameter and the Taylor series expansion combines with ordinary differential equation for the time domain analysis. An efficient method (referred as "Present Method") for a better accuracy evaluation of TDGF has been proposed. The numerical results generated from precise integration method and analytical solution of Shan et al. (2019) revealed that the "Present method" provides a better solution in the computational domain. The comparison of the heave hydrodynamic coefficients in solving the radiation problem of a hemisphere at zero speed between the "Present method" and the analytical solutions proposed by Hulme (1982) showed that the difference of result is small, less than 3%.