• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.285-297
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• 2013

This paper deals with parabolic equations coupled via nonstandard growth sources, subject to homogeneous Dirichlet boundary conditions. Three kinds of necessary and sufficient conditions are obtained, which determine the complete classifications for non-simultaneous and simultaneous blowup phenomena. Moreover, blowup rates are given.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.615-640
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• 2016

We consider the fourth-order $Schr{\ddot{o}}dinger$ equation with focusing inhomogeneous nonlinearity ($-{\mid}x{\mid}^{-2}{\mid}u{\mid}^{\frac{4}{n}}u$) in high space dimensions. Extending Glassey's virial argument, we show the finite time blowup of solutions when the energy is negative.

• International Journal of Highway Engineering
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• v.20 no.3
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• pp.65-73
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• 2018

PURPOSES : In this study, the propriety of expansion joint spacing of airport concrete pavement was examined by using weather and material characteristics. METHODS : A finite element model for simulating airport concrete pavement was developed and blowup occurrence due to temperature increase was analyzed. The critical temperature causing the expansion of concrete slab and blow up at the expansion joint was calculated according to the initial vertical displacement at the joint. The amount of expansion that can occur in the concrete slab for 20 years of design life was calculated by summing the expansion and contraction by temperature, alkali-silica reaction, and drying shrinkage. The effective expansion of pavement section between adjacent expansion joints was calculated by subtracting the effective width of expansion joint from the summation of the expansion of the pavement section. The temperature change causing the effective expansion of pavement section was also calculated. The effective expansion equivalent temperature change was compared to the critical temperature, which causes the blowup, according to expansion joint spacing to verify the propriety of expansion joint applied to the airport concrete pavement. RESULTS : When an initial vertical displacement of the expansion joint was 3mm or less, the blowup never occurred for 300m of joint spacing which is used in Korean airports currently. But, there was a risk of blow-up when an initial vertical displacement of the expansion joint was 5mm or more due to the weather or material characteristics. CONCLUSIONS : It was confirmed that the intial vertical displacement at the expansion joint could be managed below 3mm from the previous research results. Accordingly it was concluded that the 300m of current expansion joint spacing of Korean airports could be used without blowup by controling the alkali-silica reaction below its allowable limit.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.929-941
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• 2000

We study a parabolic system of chemotaxis introduced by E.F. Keler and L.A. Segel. First, norm behaviors of the blow-up solution are proven. Then some kind of symmetry breaking and the concentration toward the boundary follow when the L$^1$norm of the initial value is less than 8$\pi$. Meanwhile a method of rearrangement is porposed toprove an inequality of Trudinger-Moser's type.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.721-733
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• 2000

A paeabolic-elliptic system modelling chemotaxis is analysed. We study the behavior of solutions, especially the finite-time blowup of nonradial dolutions, to parabolic-elliptic system of n(n 2).

• Journal of the Korea Institute of Information Security & Cryptology
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• v.23 no.3
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• pp.395-404
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• 2013

A pattern matching algorithm plays an important role in traffic identification and classification based on predefined patterns for intrusion detection and prevention. As attacks become prevalent and complex, current patterns are written using regular expressions, called regexes, which are expressed into the deterministic finite automata(DFA) due to the guaranteed worst-case performance in pattern matching process. Currently, because of the increased complexity of regex patterns and their large number, memory-efficient DFA from states reduction have become the mainstay of pattern matching process. However, most of the previous works have focused on reducing only the number of states on a single automaton, and thus there still exists a state blowup problem under the large number of patterns. To solve the above problem, we propose a new state compression algorithm that merges states on multiple automata. We show that by merging states with the same input character on multiple automata, the proposed algorithm can lead to a significant reduction of the number of states in the original DFA by as much as 40.0% on average.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.45-61
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• 2009

We consider finite time blowup solutions of the $L^2$-critical focusing Hartree equation on $\mathbb{R}^n$, $n{\geq}3$ below $H^1$.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.779-786
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• 2007

In this note, we consider a system of two reaction-diffusion equations with absorption, under homogeneous Dirichlet boundary. Using scaling methods, we establish the blow-up rate estimates.

• Proceedings of the Korean Society of Laser Processing Conference
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• 2006.06a
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• pp.35-40
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• 2006

Laser welding is high power density welding method which is higher speed and productivity, lower thermal deformation, without material restrictions for car body welding. But, in case of zinc coated sheet metal welding, the gap is needed $0.1{\sim}0.2mm$ to avoid weld bead blowup. This paper describe that it used dimple and pressure roller tool to improve laser welding quality for 3-layer zinc coated sheet metal.