• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.901-906
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• 2013

In this paper, we show that if a nontrivial transitive set is $C^1$-stably measure expansive, then it admits a dominated splitting.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.65-71
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• 2010

Let $\Lambda$ be a transitive set for f. In this paper, we show that if a f-invariant set $\Lambda$ has the $C^{1}$-stably shadowing property, then $\Lambda$ admits a dominated splitting.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.285-291
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• 2011

In this paper, we show that if a transitive set ${\Lambda}$ is $C^1$-stably expansive, then ${\Lambda}$ admits a dominated splitting.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.177-181
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• 2017

Let $f:M{\rightarrow}M$ be a diffeomorphism of a compact smooth manifold M. In this paper, we show that $C^1$ generically, if a chain transitive set ${\Lambda}$ is locally maximal then it admits a dominated splitting. Moreover, $C^1$ generically if a chain transitive set ${\Lambda}$ of f is locally maximal then it has zero entropy.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.735-743
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• 2011

Let f be a diffeomorphism of a closed n-dimensional smooth manifold. In this paper, we introduce the notion of $C^1$-stably periodic shadowing property for a closed f-invariant set, and prove that for a transitive set ${\Lambda}$, if f has the $C^1$-stably periodic shadowing property on ${\Lambda}$, then ${\Lambda}$ admits a dominated splitting.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.617-623
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• 2010

Let p be a hyperbolic periodic point of f, and let ${\Lambda}(p)$ be a closed set which containing p. In this paper, we show that $C^1$-generically, if $f{\mid}_{{\Lambda}(p)}$ has the $C^1$-stably asymptotic average shadowing property, then it admits a dominated splitting.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.581-587
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• 2013

Let ${\Lambda}$ be a robustly transitive set of a diffeomorphism $f$ on a closed $C^{\infty}$ manifold. In this paper, we characterize hyperbolicity of ${\Lambda}$ in $C^1$-generic sense.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.165-170
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• 2019

$C^1$ generically, if a diffeomorphism $f:M{\rightarrow}M$ of a closed smooth Riemannian manifold M has the asymptotic average shadowing property or the average shadowing property then f has a decomposition property.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.1-15
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• 2002

Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.22-27
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• 2006

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third-order QUICKEST explicit finite difference schemes respectively to solve the pure advection equation in order to prevent the occurrence of numerical oscillations. Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes are applied to experimental data for simulating the 2D mixing in a straight trapezoidal channel to test the model capability. Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.