• 대한수학회보
• /
• 제57권2호
• /
• pp.281-294
• /
• 2020

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

• East Asian mathematical journal
• /
• 제22권2호
• /
• pp.171-188
• /
• 2006

We consider the problem of an optimal control of the wave equation with a localized nonlinear dissipation. An optimal control is used to bring the state solutions close to a desired profile under a quadratic cost of control. We establish the existence of solutions of the underlying initial boundary value problem and of an optimal control that minimizes the cost functional. We derive an optimality system by formally differentiating the cost functional with respect to the control and evaluating the result at an optimal control.

• 대한수학회논문집
• /
• 제31권3호
• /
• pp.519-532
• /
• 2016

We consider the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations with infinite delays. We prove the existence of a pullback $\mathcal{D}$-attractor for the continuous process associated to the problem with respect to a large class of non-autonomous forcing terms.

• Nonlinear Functional Analysis and Applications
• /
• 제26권1호
• /
• pp.35-64
• /
• 2021

In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.

• 대한전기학회논문지
• /
• 제38권12호
• /
• pp.1033-1047
• /
• 1989

A finite element method for the analysis of magnetic fields with hysteresis characteristics is proposed. The method employs Preisach model to describe hysteresis of magnetic material, so that even multi-branch or minor-loop characteristics can be taken into account. The problem can be considered as the analysis of a nonlinear equation where magnetization depends not only on the present value of the magnetic field but also on the past values, and the problem can be solved by the iteration method. Measurements were carried out on soft ferrite EI core for the comparison with computer solution, and good agreements were obtained. is investigated. A theoretical approach to gait study is proposed in which the static stability margins for periodic gaits are expressed in terms of the kinematic gait formula. The effects fo the stride length on static stability are analyzed and the relations between static stability and initial body configurations are examined. It is shown that the moving velocity can be increased to some extent without affecting stability margins for a given initial body configuration. Computer simulations are performed to verify the analysis.

• 제어로봇시스템학회논문지
• /
• 제10권12호
• /
• pp.1241-1248
• /
• 2004

A controller of wheeled mobile robot(WMR) based on Lyapunov theory is designed and a Fuzzy-Neural Network algorithm is applied to this system to adjust controller gain. In conventional controller of WMR that adopts fixed controller gain, controller can not pursuit trajectory perfectly when initial condition of system is changed. Moreover, acquisition of optimal value of controller gain due to variation of initial condition is not easy because it can be get through lots of try and error process. To solve such problem, a Fuzzy-Neural Network algorithm is proposed. The Fuzzy logic adjusts gains to act up to position error and position error rate. And, the Neural Network algorithm optimizes gains according to initial position and initial direction. Computer simulation shows that the proposed Fuzzy-Neural Network controller is effective.

• 대한수학회지
• /
• 제49권5호
• /
• pp.893-905
• /
• 2012

Kirsi Majava and Xue-Cheng Tai [12] proposed a modified level set method for solving a free boundary problem associated with unilateral obstacle problems. The proximal bundle method and gradient method were applied to solve the nonsmooth minimization problems and the regularized problem, respectively. In this paper, we extend this approach to solve the bilateral obstacle problems and employ Rung-Kutta method to solve the initial value problem derived from the regularized problem. Numerical experiments are presented to verify the efficiency of the methods.

• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.97-113
• /
• 2004

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 추계학술대회
• /
• pp.1288-1293
• /
• 2004

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach of adopting the genetic algorithm as an initial value selector, whereas using the conjugate-gradient method and Newton method to reduce their dependence on the initial value.

• Applied Microscopy
• /
• 제43권1호
• /
• pp.1-8
• /
• 2013

We developed an improved method for tilt series alignment with fiducial markers in electron tomography. Based on previous works regarding alignment, we adapted the Levenberg-Marquardt method to solve the nonlinear least squares problem by incorporating a new formula for the alignment model. We also suggested a new method to estimate the initial value for inversion with higher accuracy. The proposed approach was applied to geopolymers. A better alignment of the tilt series was achieved than that by IMOD S/W. The initial value estimation provided both stability and a good rate of convergence since the new method uses all marker positions, including those partly covering the tilt images.