• 대한수학회지
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• 제59권6호
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• pp.1171-1184
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• 2022

We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.

• 대한수학회보
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• 제44권3호
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.363-374
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• 2007

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

• 충청수학회지
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• 제28권1호
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• pp.161-172
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• 2015

In this paper, we consider the chemotaxis-haptotaxis model of tumor invasion with the proliferation and tissue re-establishment term in dimensions one and two. We show the global in time existence of a unique classical solution for the the model in two dimensional spatial domain without any restrictions on the coefficients.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.1041-1044
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• 1998

In this paper the cellular neural networks with annealing capability is designed. The annealing capability helps the networks escape from the local-minimum points and quickly search for the global-minimum point. A 6$\times$6 CNN chip is designed using a $0.8\mu\textrm{m}$ CMOS technology, and the chip area is 2.89mm$\times$2.89mm. The simulation results for hole filling image processing show that the general CNN has a local-minimum problem, but the annealed CNN finds the global-minimum solutions very efficiently.

• 대한수학회지
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• 제42권6호
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• pp.1137-1152
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• 2005

In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

• 대한수학회보
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• 제50권6호
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• pp.1765-1780
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• 2013

This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

• 대한수학회보
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• 제50권3호
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• pp.811-821
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• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• 대한수학회지
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• 제54권6호
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• pp.1787-1799
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• 2017

In this paper, we prove basic a priori estimate for the ${\bar{\partial}}$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the ${\bar{\partial}}$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.

• 대한수학회지
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• 제46권1호
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• pp.31-39
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• 2009

A bifurcation problem for nonlinear partial differential equations of the form $$div({\varphi}(|{\nabla}u|){\nabla}u+{\mu}_0{\varphi}(|u|)u=q({\lambda},\;x,\;u,\;{\nabla}u)$$ subject to Dirichlet boundary conditions is discussed. Using a global bifurcation theorem of Rabinowitz type, we show that under certain conditions on $\varphi$ and q, the above equation has an unbounded connected set of solutions (u, $\lambda$).