• 대한수학회보
• /
• 제60권2호
• /
• pp.425-441
• /
• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Journal of Mechanical Science and Technology
• /
• 제14권2호
• /
• pp.168-176
• /
• 2000

Related to the error dynamics of an adaptive system, averaging theorems are developed for coupled differential equations which consist of ordinary differential equations and a parabolic partial differential equation. The results are then applied to the convergence analysis of the parameter estimate errors in the model reference adaptive control of a nonautonomous parabolic partial differential equation with lowly time-varying parameters.

• 대한수학회보
• /
• 제42권4호
• /
• pp.829-836
• /
• 2005

In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

• Journal of the Korean Statistical Society
• /
• 제31권3호
• /
• pp.329-342
• /
• 2002

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

• 호남수학학술지
• /
• 제27권2호
• /
• pp.205-209
• /
• 2005

In this paper we discuss on the uniquenss of the solution of partial differential equations: (1) $${\frac{{\partial}w}{{\partial}{\bar{z}}}}=F(z,\;w,\;{\frac{{\partial}w}{{\partial}z}}}+G(z,\;w.{\bar{w})$$ in the sobolev space $W_{1,p}(D)$.

• Journal of information and communication convergence engineering
• /
• 제2권3호
• /
• pp.187-192
• /
• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• 호남수학학술지
• /
• 제45권1호
• /
• pp.1-24
• /
• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• Wind and Structures
• /
• 제28권6호
• /
• pp.347-354
• /
• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Journal of the Korean Statistical Society
• /
• 제25권2호
• /
• pp.161-173
• /
• 1996

When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

• 호남수학학술지
• /
• 제30권4호
• /
• pp.631-635
• /
• 2008

In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.