• Honam Mathematical Journal
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• v.43 no.4
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• pp.667-678
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• 2021

Blow-up phenomena for a nonlocal reaction-diffusion system with time-dependent coefficients are investigated under null Dirichlet boundary conditions. Using Kaplan's method with the comparison principle, we establish new blow-up criteria and obtain the upper bounds for the blow-up time of the solution under suitable measure sense in the whole-dimensional space.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.137-147
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• 2022

In this paper, we considered the Dirichlet initial boundary value problem of a nonlinear viscoelastic wave equation with nonlinear damping and source terms, and investigated finite time blow-up phenomena of the solutions to the equation with arbitrary positive initial data, under suitable conditions.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1143-1158
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• 2020

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source u_t - △u - △u_t = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ ℝⁿ (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.287-308
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• 2018

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.267-296
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• 2018

This paper studies the Cauchy problem and blow-up phenomena for a new generalized Camassa-Holm equation with cubic nonlinearity in the nonhomogeneous Besov spaces. First, by means of the Littlewood-Paley decomposition theory, we investigate the local well-posedness of the equation in $B^s_{p,r}$ with s > $max\{{\frac{1}{p}},\;{\frac{1}{2}},\;1-{\frac{1}{p}}\},\;p,\;r{\in}[0,{\infty}]$. Second, we prove that the equation is locally well-posed in $B^s_{2,r}$ with the critical index $s={\frac{1}{2}}$ by virtue of the logarithmic interpolation inequality and the Osgood's Lemma, and it is shown that the data-to-solution mapping is $H{\ddot{o}}lder$ continuous. Finally, we derive two kinds of blow-up criteria for the strong solution by using induction and the conservative property of m along the characteristics.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.773-784
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• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1105-1119
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• 2010

We consider jump processes which has only downward jumps with size a fixed fraction of the current process. The jumps of the pro cesses are interpreted as crashes and we assume that the jump intensity is a nondecreasing function of the current process say $\lambda$(X) (X = X(t) process). For the case of $\lambda$(X) = $X^{\alpha}$, $\alpha$ > 0, we show that the process X shold explode in finite time, say $t_e$, conditional on no crash For the case of $\lambda$(X) = (lnX)$^{\alpha}$, we show that $\alpha$ = 1 is the borderline of two different classes of processes. We generalize the model by adding a Brownian noise and examine the blow up properties of the sample paths.

• The Journal of the Acoustical Society of Korea
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• v.34 no.4
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• pp.328-334
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• 2015

This paper describes an acoustic analysis of a Jing, Korean percussion instrument, according to different drive point and blow strength, and this analysis is focused on the softening and beat phenomena. Three kinds of blow strength (very strong, strong, and weak) and three locations of drive point (center, up, and right) are applied, and the spectrogram function built in Matlab is utilized to analyzing the softening and beat of target sounds. The stronger blow you drive to the center of the Jing, the more clearly softening is observed. Frequency shifting is increased proportionally to the blow strength and frequency and it is stand out on the harmonics in contrast with that of other partials. Beat of the Jing can be classified into the early beat and late beat. The beats by the outside driven Jing are distributed in wider frequency band than the beats by the center driven Jing. In addition, it is observed that the early beat is affected by few specific partials developed around harmonics for the center driven Jing.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• Journal of Energy Engineering
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• v.4 no.2
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• pp.261-269
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• 1995

본 연구에서는 밀폐형 2상 열사이폰의 액체 Pool에서 발생하는 핵비등현상과 유동영역에 대해 가시화 방법으로 연구하였다. 실험용 열사이폰은 스텐레스와 유리관을 이용하여 제작하였으며, 열공급은 증발부 주위에 설치된 유도 가열용 코일에 고주파를 가함으로써 스텐레스 외면에 발열이 일어나도록 하였다. 이에 따른 결과는 다음과 같다. 실험용 열사이폰은 고주파 가열등 열사이폰의 작동성능을 저해하는 여러 요인들이 포함되어 있었으나, 실험결과 이러한 문제는 실험 내용에 영향을 미칠만큼 크게 나타나지 않았다. 열속과 상당압력의 범위는 각각2$m^2$, 0.1