• 호남수학학술지
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• 제43권4호
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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.

• 대한수학회보
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• 제50권6호
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• pp.1765-1780
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• 2013

This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권4호
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• pp.243-248
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• 2012

We consider the (possible) finite time blow-up of the smooth solutions of the 3D incompressible Euler equations in a smooth domain or in $R^3$. We derive blow-up criteria in terms of $L^{\infty}$ of the partial component of Hessian of the pressure together with partial component of the vorticity.

• 대한수학회보
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• 제55권1호
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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.

• Archives of Plastic Surgery
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• 제34권1호
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• pp.44-51
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• 2007

Purpose: Blow-out fracture is one of the most common fractures in facial trauma. It is diagnosed by Computed Tomography(CT) scan, which is considered as the most effective diagnostic tool. Since, the Picture Archiving Communication System(PACS) has been provided recently to many hospitals, doctors are more familiar with imaging software of PACS. Because this software has many useful measuring tools, doctors can measure orbital structure easily and make a plan for treatment with its data. Therefore, authors intended to analyze the data of orbital structure measured with PACS imaging software and evaluate its usefulness. Methods: The charts and CT images of 100 patients, which were 50 patients with medial wall fracture and 50 patients with floor fracture, were reviewed. Patients were selected by pre-determined criteria and their CT images were measured with image software of PACS. 'Extraocular muscle thickness', 'Defect ratio'(ratio of defect area to normal area) and 'Globe position index' were measured and analyzed statistically. Results: The thickness of inferior rectus muscle and medial rectus muscle was simultaneously increased in acute-stage of blow-out fracture. The medial rectus muscle was more thickened in medial wall fracture and inferior rectus was more thickened in floor fracture, respectively. In acute blow-out fracture, globe position is exophthalmic rather than enophthalmic. Especially in floor fracture, numerical value summed up thickness of all extraocular muscle is correlated to the defect ratio and globe position index. Conclusion: Clinicians can decide globe position or presume defect ratio in inferior wall fracture by measurement of CT image in acute blow-out fracture using PACS.