• 대한수학회논문집
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• 제30권3호
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• pp.201-208
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• 2015

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).

• 대한수학회보
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• 제58권6호
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• pp.1445-1461
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• 2021

The aim of this paper is to show the local well-posedness of 2 dimensional Dirac equations with power type and Hartree type nonlin-earity derived from honeycomb structure in H^s for s > $\frac{7}{8}$ and s > $\frac{3}{8}$, respectively. We also provide the smoothness failure of flows of Dirac equations.

• Journal of the Korean Physical Society
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• 제73권11호
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• pp.1631-1636
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• 2018

Unpolarized 1.047-GeV proton inelastic scatterings from the Ni isotopes $^{62}Ni$ and $^{64}Ni$ are analyzed phenomenologically employing an optical potential model and the first-order collective model in the relativistic Dirac coupled channel formalism. The Dirac equations are reduced to $Schr{\ddot{o}}dinger-like$ second-order differential equations, and the effective central and spin-orbit optical potentials are analyzed by considering the mass-number dependence. The multistep excitation via the $2^+$ state is found to be important for the $4^+$ state excitation in the ground state rotational band for proton inelastic scatterings from the Ni isotopes. The calculated deformation parameters for the $2^+$ and the $4^+$ states of the ground state rotational band and for the first $3^-$ state are found to agree pretty well with those obtained from nonrelativistic calculations.

• 대한수학회지
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• 제53권6호
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• pp.1347-1370
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• 2016

On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1{\geq}5$, $m{\equiv}0$ mod 2, we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair (${\varphi}_{{\frac{m}{2}}-1}$, ${\varphi}_{\frac{m}{2}}$) of spinor fields (called Sasakian duo, see Definition 2.1) that solves a special system of two differential equations.

• 대한수학회논문집
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• 제33권3호
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• pp.871-888
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• 2018

We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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• pp.147-148
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• 2005

In this paper we study Laplace transform of the fuzzy Dirac delta function and the examples of fuzzy impulsive differential equations.

• 호남수학학술지
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• 제17권1호
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• pp.107-118
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• 1995

We study the asymptotic behavior of nonnegative singular solutions of semilinear parabolic equations of the type $$u_t={\Delta}u-(u^q)_y-u^p$$ defined in the whole space $x=(x,y){\in}R^{N-1}{\times}R$ for t>0, with initial data a Dirac mass, ${\delta}(x)$. The exponents q, p satisfy $$1 where $q^*=max\{q,(N+1)/N\}$.

• 대한기계학회논문집A
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• 제27권5호
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• pp.833-839
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• 2003

The effects of stiffeners on the modal characteristics of rectangular plates are investigated. A modeling method for the modal analysis of rectangular plates with stiffeners is presented. A mass density Dirac's delta function is used to idealize the stiffeners mathematically. The equations of motion for the plates are derived and transformed into a dimensionless form. To confirm the accuracy of the method presented in this study, numerical result are obtained and compared to those of a commercial program. The mode shape variations due to some parameter variations are also exhibited.

• 대한수학회지
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• 제37권6호
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• pp.1071-1084
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• 2000

We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂$^2$(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.

• Interaction and multiscale mechanics
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• 제6권3호
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• pp.287-300
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• 2013

In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.