• Journal for History of Mathematics
• /
• v.16 no.4
• /
• pp.107-115
• /
• 2003

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.393-401
• /
• 2014

In this work, we discuss the existence of mild solutions in the ${\alpha}$-norm for some partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

• 전기의세계
• /
• v.28 no.1
• /
• pp.53-58
• /
• 1979

In the microwave heating system, a ferroresonant transformer is used to regulate the magnetron power fluctuation. For the simplification, nonlinear characteristics of the transformer and the magnetron are idealized to be piecewise linear. Dipped peak shape of the magnetron current is explained qualitatively by considering the fundamental and third harmonic frequency components in the circuit. Design equations providing the values of the leakage inductance, turn ratio of the transformer and the capacitance are derived analytically by cosnidering the fundamental frequency component only. The ferroresonant transformer is designed to obtain a required regulation and high input power factor from the derived design equations, and analytical calculations are compared with experimental measurements.

• 한국방재학회:학술대회논문집
• /
• 2008.02a
• /
• pp.237-240
• /
• 2008

Numerical Analysis for exchanging seawater experiment is carried out in Do-Jang fish port. The change of tidal velocity and water level is derived by the two-dimensional nonlinear shallow-water numerical model. To calculate exchange rate of seawater with the change of tidal velocity and water level, a two-dimensional numerical model is employed which governing equations are Fokker-Plank equations. The calculated exchange rates of each time are described in tables and figures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.11a
• /
• pp.649-654
• /
• 2000

The non-linear differential equations of motion of a fluid conveying curved pipe are derived by making use of Hamiltonian approach. The extensible dynamics of the pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the basic analysis results are discussed. Using eigenfrequency analysis, it can be shown that the natural frequencies are changed with flow velocity.

• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.207-214
• /
• 2011

The formal linearization method is an efficient method for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, we obtain multisoliton solution of generalization Burger's equation and the (3+1)-dimension Burger's equation and the Boussinesq equation by the formal linearization method.

• Proceedings of the KIPE Conference
• /
• 2019.07a
• /
• pp.483-484
• /
• 2019

This paper proposes a harmonic state space (HSS) modeling of DC microgrid. In the HSS model, nonlinear equations for the switched circuit model are transformed into multiple linear equations. The simulation results have shown the HSS modeling is comparable with PSIM simulation.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.3
• /
• pp.649-662
• /
• 2022

This paper is concerned with the existence of solutions for a class of 𝚽-Kirchhoff type equations with critical exponent in Orlicz-Sobolev spaces. Our technical approach is based on variational methods.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.510-515
• /
• 2000

Dynamic stability of a flying structure undertaking constant and pulsating axial forces is investigated in this paper. The equations of motion of the structure, which is idealized as a free-free beam, are derived by using the hybrid variable method and the assumed mode method. The structural system includes a directional control unit to obtain the directional stability. The analysis model presented in this paper considers the nonlinear effect due to rigid body motion of the beam. Dynamic stability of the system is influenced by the nonlinear effect. In order to examine the nonlinear effect, first the unstable regions of the linear system are obtained by using the method based upon Floquet's theory, and dynamic responses of the nonlinear system in the unstable region are obtained by using direct time integration method. Dynamic stability of the nonlinear system is determined by the obtained dynamic responses.

• International Journal of Aeronautical and Space Sciences
• /
• v.4 no.1
• /
• pp.53-62
• /
• 2003

In this study, nonlinear aeroelastic characteristics of an supersonic missile wing with strong shock interferences are investigated. The missile wing model has a freeplay structural nonlinearity at its pitch axis. To practically consider the effects of freeplay structural nonlinearity, the fictitious mass method is applied to structural vibration analysis based on finite element method. Nonlinear aerodynamic flows with unsteady shock waves are also considered in supersonic flow regions. To solve the nonlinear aeroelastic governing equations including the freeplay effect, a modal-based coupled time-marching technique based on the fictitious mass method is used in the time-domain. Various aeroelastic computations have been performed for the nonlinear wing structure model. Linear and nonlinear aeroelastic analyses have been conducted and compared with each other in supersonic flow regions. Typical nonlinear limit cycle oscillations and phase plots are presented to show the complex vibration phenomena with simultaneous fluid-structure nonlinearities.