• Journal for History of Mathematics
• /
• v.31 no.5
• /
• pp.211-222
• /
• 2018

This paper surveys the theory of symmetry group of differential equations. A proof of the simplest version of the Noether's theorem on conservation laws has been presented with examples in the classical mechanics. As a new approach to the conservation laws the theory of characteristic cohomology due to S. H. Wang and others has been presented.

• Journal of the Chungcheong Mathematical Society
• /
• v.10 no.1
• /
• pp.71-85
• /
• 1997

In this paper we find sufficient conditions of existence of the nonlinear ODE ($P_{\epsilon}$) which is induced by the nonlinear hyperbolic system of conservation laws in several space variables.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.73-93
• /
• 1999

In this paper we prove the existence of solutions for the nonlinear hyperbolic system of conservation laws in several space variables provided that the initial data are very close to each other. We also give an example and discuss the existence of solutions for large initial data.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.521-530
• /
• 1996

This paper treats the existence of odd solutions of the Cauchy problem for a perturbation of a conservation law.

• Journal of Environmental Science International
• /
• v.13 no.10
• /
• pp.871-882
• /
• 2004

Korea's national park system resembles that of Japan in many ways. In this study, National park Systems of the two countries are compared from a standpoint of their historical backgrounds to be formed and in aspect of its conservation by the main revision of national park laws in perspective. In conclusion it was found out that Korea's toleration-based regulations on building park amenities have gradually neglected the park conservation effort, whereas Japan's authorization-oriented regulations have streng thened their emphasis on park conservation. From the comparison as above, the polices to be modified for Korean national park are proposed as follows: 1. National park system, which values diversity of species, is to be proposed. For this, the Article 8 which allows a development of National parks, Enforcement Ordinance Article 4, The Article 18 of Law, Enforcement Regulation Article 6 & 7 of National Park Law should be reviewed for deletion and revision. 2. On the basis of the laws, zoning system should be readjusted by discriminated conservation policy. Also, the readjustment of zoning system should be enforced after thorough analysis and research on the value of natural resources in the national park. 3. Korea should closely review the recently revised Japanese laws on the national parks and nature revitalization promotion for applying them to conservation policy of Korean national parks.

• Korean Journal of Environment and Ecology
• /
• v.11 no.1
• /
• pp.18-36
• /
• 1997

This study was conducted to analyze the text relating to the environmental conservation and ecology among the text of the constitution of Korea and collect the domestic laws(40 statutes, 1 guide, 1 leading case) and the foreign laws(1 constitution, 34 statutes, 2 ordinances, 3 leading cases). To make the text of the collected domestic and foreign laws a comparative analysis of the conceptual principle, plan establishment and project operation, types, policy and allied projects, rights and duties, allowed and restricted acts, environmental impact assessment and administration procedure and system of the environmental conservation and ecology by items, it was considered to the mutual relation with lots of laws which are scattered with the various laws and studied to how to set the many foreign countries on their laws connected with the environmental conservation and ecology from the other department and carry out the advanced environmental works.

• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.37-59
• /
• 1998

We prove that solutions $u^\epsilon$ for the mixed hyperbolic-elliptic system of conservation laws with the viscosity term are total variation bounded uniformly in $\epsilon$ and that the solution $u^\epsilon$ converges to the solution for the mixed hyperbolic-elliptic Riemann problem as $\epsilon \to 0$.

• Communications of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.145-155
• /
• 2007

In this paper, we show the convergence of approximate solutions to the convective porous media equation using methodology developed in [8]. First, we obtain the approximate transport equation for the given convective porous media equation. Then using the averaging lemma, we obtain the convergence.

• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.85-114
• /
• 1998

We prove the existence of solutions of the Reimann problem for a system of conservation laws of mixed type using the method of vanishing viscosity term.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.3
• /
• pp.211-236
• /
• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.