• 대한수학회보
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• 제35권4호
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• pp.689-700
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• 1998

We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• 대한수학회보
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• 제58권6호
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• pp.1539-1561
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• 2021

We prove Perelman type 𝒲-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• 대한수학회논문집
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• 제20권1호
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• pp.179-193
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• 2005

We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing up an inclined plane. Equations of the type $h_t+f_y(h) = -{\in}^3{\nabla}{\cdot}(M(h){\nabla}{\triangle}h)$ arise in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, t) is the fluid film height. A hybrid scheme is constructed for the solution of two-dimensional higher-order nonlinear diffusion equations. Problems in the fluid dynamics of thin films are solved to demonstrate the accuracy and effectiveness of the hybrid scheme.

• 한국정보과학회논문지:소프트웨어및응용
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• 제32권6호
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• pp.523-531
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• 2005

확산(Diffusion)을 이용한 기존의 칼라영상 분할은 확산의 횟수가 반복될수록 경계선 정보가 적절히 유지되지 못하거나 잡음을 제거하지 못함으로써 워터쉐드(Watershed) 알고리즘을 적용하는 경우, 과분할을 피할 수 없다는 단점을 갖고 있다. 본 논문에서는 수리 형태학(Mathematical Morphology)과 비선형 확산(Non-Linear Diffusion)을 함께 적용하여 과분할의 문제점을 제거한 워터쉐드 결과를 얻을 수 있는 칼라영상 분할방법을 제안한다. 임의의 칼라 영상을 LUV 색상공간으로 변환하여, 그 각각의 색상공간에 수리 형태학을 응용한 재구성에 의한 닫힘(Reconstruction) 연산과 비선형 확산을 함께 적용하여 경계선을 적절히 유지하면서 잡음을 제거한 단순 영상을 획득할 수 있다. 이 영상에서 칼라 영상의 기울기(Gradient) 정보를 획득하고, 워터쉐드 알고리즘을 적용하여 영상을 분할한다. 실험 결과, 기존의 방법보다 과분할이 현저히 제거되고, 칼라 영상이 매우 효과적으로 분할됨을 확인하였다

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.747-752
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• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• Nuclear Engineering and Technology
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• 제31권2호
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• pp.151-156
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• 1999

Under the heavy irradiation of crystalline materials when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriate transformation of these nonlinear differential equations to more solvable Poisson's equations, finally analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2003년도 봄 학술발표회 논문집
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• pp.321-326
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• 2003

The nonlinear humidity distribution occurs due to the moisture diffusion when a concrete is exposed to an ambient air. These nonlinear humidity distribution induces shrinkage cracks on surfaces of the concrete. Because shrinkage cracks largely affect the durability and serviceability of concrete structures, the moisture diffusion in concrete must be investigated. The purpose of this paper is to propose a model of the moisture diffusion coefficient that governs moisture diffusion within concrete structures. To propose the model, numerical analysis were performed based on several experiments. Because the moisture diffusion coefficient is changed with aging, especially at early ages, the proposed model includes aging effect by terms of the porosity as well as the humidity of concrete.

• Journal of the Korean Statistical Society
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• 제29권4호
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• pp.489-499
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• 2000

We propose a new instrumental variable estimator of the complex parameter of a class of univariate complex-valued diffusion processes defined by the possibly non-stationary and/or nonlinear stochastic differential equations. On the basis of the exact finite sample distribution of the pivotal quantity, we construct the exact confidence intervals and the exact tests for the parameter. Monte-Carlo simulation suggests that the new estimator seems to provide a viable alternative to the maximum likelihood estimator (MLE) for nonlinear and/or non-stationary processes.