• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1017-1029
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• 2019

In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $({\varrho}(u))_t$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.67-78
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• 1998

• 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.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.529-540
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• 2008

This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system, $${u_t}-{\triangle}_{m,p}u=u^{{\alpha}_1}\;{\int}_{\Omega}\;{\upsilon}^{{\beta}_1}\;(x,\;t)dx,\;{\upsilon}_t-{\triangle}_{n,p}{\upsilon}={\upsilon}^{{\alpha}_2}\;{\int}_{\Omega}\;u^{{\beta}_2}\;(x,{\;}t)dx,$$ with homogeneous Dirichlet boundary condition. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system.

• Journal of Environmental Science International
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• v.14 no.1
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• pp.41-51
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• 2005

Using three-dimensional non-hydrostatical numerical model with one way double nesting technique, atmo­spheric circulation in the mountainous coastal region in summer was investigated from August 13 through 15, 1995. During the day, synoptic westerly wind blows over Mt. Mishrung in the west of a coastal city, Sokcho toward the East Sea, while simultaneously, easterly upslope wind combined with both valley wind from plain (coast) toward mountain and sea-breeze from sea toward inland coast blows toward the top of the mountain. Two different directional wind systems confront each other in the mid of eastern slope of the mountain and the upslope wind goes up to the height over 2 km, becoming an easterly return flow in the upper level over the sea and making sea-breeze front with two kinds of sea-breeze circulations of a small one in the coast and a large one in the open sea. Convective boundary layer is developed with a thickness of about 1km over the ground in the upwind side of the mountain in the west and a thickness of thermal internal boundary layer from the coast along the eastern slope of the mountain is only confined to less than 200 m. On the other hand, after sunset, no prohibition of upslope wind generated during the day and downward wind combined with mountain wind from mountain towardplain and land-breeze from land toward under nocturnal radiative cooling of the ground surfaces should intensify westerly downslope wind, resulting in the formation of wind storm. As the wind storm moving down along the eastern slop causes the development of internal gravity waves with hydraulic jump motion in the coast, bounding up toward the upper level of the coastal sea, atmospheric circulation with both onshore and offshore winds like sea-breeze circulation forms in the coastal sea within 70 km until midnight and after that, westerly wind prevails in the coast and open seas.

• Atmosphere
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• v.15 no.4
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• pp.191-202
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• 2005

This study was conducted to estimate how vertically high and horizontally long a sea breeze occurred around Gangneung of the Korean peninsula would be reached to an inland. Geographically, gangneung is located on the center of the east coast shaping an arc, and a coastal line around gangneung has a form extending northwestward and southeastward, respectively. Therefore, an inflow of the northerly has similar effects of the sea breeze since a deep valley of Daegwallyeong, which is one of main ridges of the Taebaek mountains, not only reaches northeastward up to this region but also plays the part of the steering gear changing a wind direction from northerly to easterly, this is, the wind from sea. First of all, the study had defined the sea breeze as a wind blown from NNE to ESE, clockwise. And then, we analyzed characteristics of the sea breeze occurred around gangneung in view of the maximum wind speed and the wind direction for October 1st, 2003 through September 30th, 2004, the upper air database for May through June of 2004, and the wind vector database of AWS (Automatic Weather System). All meteorological information is collected at the weather station of gangneung and by the AWS which is being scattered around this region. Finally, the study figures out that how horizontally long a sea breeze would be reached depends on a level of the easterly inflow. At the first step of the inflow of the sea breeze, the wind from NNW blows into this region by keeping up the speed $3m{\cdot}s^{-1}$, and effects of the northerly are dominated with time and the wind at the inland blows out southwestward cause of the surface friction at the next step. On the other hand, there is no change of wind direction in the inflow at Daegwallyeong because a surface friction of there is smaller than around gangneung, relatively. In other word, the easterly blows toward Daegwallyeong. However, the wind speed is not higher than that of the coast around gangneung.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2119-2139
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• 2017

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.105-116
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• 2013

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, then every positive solution blows up in finite time, but for $q$ > $q_c$, there exist both global and non-global solutions to the problem.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1299-1322
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• 2020

We consider closed, star-shaped, admissible hypersurfaces in ℝⁿ⁺¹ expanding along the flow Ẋ = |X|^α-1 F^-β, α ≤ 1, β > 0, and prove that for the case α ≤ 1, β > 0, α + β ≤ 2, this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a round sphere after rescaling. Besides, for the case α ≤ 1, α + β > 2, if furthermore the initial closed hypersurface is strictly convex, then the strict convexity is preserved during the evolution process and the flow blows up at finite time.

• Journal of Environmental Science International
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• v.7 no.3
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• pp.369-374
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• 1998

Meteorological measurements were carried out in the basin of Cheong-Kwan located Yang-San near Pusan city, from Oct. 30 to Nov. 1, 1988. According to the measured data, we vended the close relationship between the variation of nocturnal Inversion layer and the meteorological elements. The nocturnal intrersion layer by radiative cooling in this site extends up to 130 meters or so. And the nocturnal jet ap- pears just above or at the top of the inversion layer, and the stronger of the prevailing wind blows, and the lower of the jet level appears. Some meteorological features such as heating, cooling etc., began to change in or in the slightly higher level of the inversion layer, when they are formed, reinforced and disappeared. And the it In the basin preserves its character because It Is not affected by local scale air flow.