• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2006.07a
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• pp.482-482
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• 2006

• Honam Mathematical Journal
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• v.24 no.1
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• pp.35-41
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• 2002

The solutions of a homogeneous system in state space form $\dot{x}=Ax$ are to the form $x=e^{At}x_0$ and the solutions of an inhomogeneous system $\dot{x}=Ax(t)+f(t)$ are to the form $x=e^{At}x_0+{{\int}_0^t}\;e^{A(t-{\tau})}f({\tau})d{\tau}$. In this note we show that the solution of descriptor systems under some conditions exists, and is unique, moreover it is interesting to know the solutions of descriptor system are schematically like the solutions as in the state space form. Also we will give some algorithms to compute these solutions.

• Bulletin of the Korean Chemical Society
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• v.31 no.12
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• pp.3573-3578
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• 2010

Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schr$\ddot{o}$dinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.765-777
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• 2016

In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged O(3) sigma models. The property of solutions depends on a parameter ${\tau}{\in}[-1,1]$ appearing in the nonlinear term. The case ${\tau}=1$ lies on the borderline for the existence of solutions in the previous results [4, 5, 7]. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1{\leq}{\tau}$<1, we establish solutions which are perturbed from the solutions of singular Liouville equations.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.703-719
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• 2014

This paper is concerned with the traveling wave solutions of nonlocal dispersal models with nonlocal delays. The existence of traveling wave solutions is investigated by the upper and lower solutions, and the asymptotic behavior of traveling wave solutions is studied by the idea of contracting rectangles. To illustrate these results, a delayed competition model is considered by presenting the existence and nonexistence of traveling wave solutions, which completes and improves some known results. In particular, our conclusions can deal with the traveling wave solutions of evolutionary systems which admit large time delays reflecting intraspecific competition in population dynamics and leading to the failure of comparison principle in literature.

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1339-1345
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• 2001

Laminar film condensation of a saturated pure vapor in forced flow over a flat plate is analyzed as boundary layer solutions. Similarity solutions for some real fluids are presented as a function of modified Jakob number (C$\_$pι/ ΔΤ/Prh$\_$fg/) with property ratio (No Abstract.see full/text) and Pγ as parameters and compared with approximate solutions which were obtained from energy and momentum equations without convection and inertia terms in liquid flow. Approximate solutions agree well with the similarity solutions when the values of modified Jakob number are less then 0.1 near 1 atmospheric pressure.

• Journal of Mechanical Science and Technology
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• v.15 no.6
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• pp.752-763
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• 2001

Although there are many different solution schemes proposed for multidimensional radiative transfer, reference solutions to benchmark these methods are very rare in the literature. In this paper we produced some accurate solutions for purely absorbing gray and nongray gases including H$_2$O and CO$_2$by using the discrete transfer method with sufficiently accurate T(sub)95 quadrature set. The spectral transmittances of the mixtures of H$_2$O and CO$_2$are estimated by using the narrow band model. The gray gas solutions are obtained for different absorption coefficients, and the nongray real gas solutions are obtained for different mixture fractions of H$_2$O and CO$_2$. The numerical solutions presented in this paper are proved to be sufficiently accurate as compared to the available exact solutions and they may be used as reference solutions in evaluating various solution schemes.

• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.853-881
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• 2001

Multiplicity for doubly-periodic solutions and Dirichlet-Periodic solutions are treated.

• Preventive Nutrition and Food Science
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• v.15 no.4
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• pp.297-303
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• 2010

The present study compared the Maillard reaction products (MRPs) derived from aqueous and ethanolic fructoseglycine and its oligomer (dimer and trimer) solutions. The pH was lower in glycine (G) than in diglycine (DG) and triglycine (TG) in both aqueous and ethanolic solutions, but the pH difference between the DG and TG was not significant. MRPs derived from the DG had a greater absorbance at 294 and 420 nm in ethanolic solution than in an aqueous solution. In particular, the loss of sugar was higher in ethanolic solution than in aqueous solution. Enolization of fructose was observed in both aqueous and ethanolic MRP solutions; however, enolization was not observed for the G in aqueous MRP solutions. The glycine oligomer content in ethanolic MRP solutions remained higher than that in aqueous MRP solutions. Furthermore, neither diglycine nor triglycine were detected in the G aqueous or ethanolic MRP solutions, while triglycine was detected in both the DG aqueous and ethanolic MRP solutions. Absorption in the ultraviolet-visible (UV-Vis) spectra was higher with MRPs derived from the ethanolic solution than with those derived from the aqueous solution. MRPs derived from the DG in an ethanolic solution showed the highest absorption intensity.