• Bulletin of the Korean Mathematical Society
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• 제49권6호
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• pp.1241-1250
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• 2012

We prove the maximum principle and the comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of $p$-harmonic functions via $p$-harmonic boundary of graphs.

• Bulletin of the Korean Mathematical Society
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• 제51권6호
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• pp.1591-1603
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• 2014

In this paper, we investigate maximum principle, convergence of sequences and angular limits for harmonic Bloch mappings. First, we give the maximum principle of harmonic Bloch mappings, which is a generalization of the classical maximum principle for harmonic mappings. Second, by using the maximum principle of harmonic Bloch mappings, we investigate the convergence of sequences for harmonic Bloch mappings. Finally, we discuss the angular limits of harmonic Bloch mappings. We show that the asymptotic values and angular limits are identical for harmonic Bloch mappings, and we further prove a result that applies also if there is no asymptotic value. A sufficient condition for a harmonic Bloch mapping has a finite angular limit is also given.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.747-756
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• 2018

We study a maximum principle for a uniformly elliptic second order differential operator in nondivergence form. We allow a bounded positive zeroth order coefficient in a certain type of unbounded domains. The results extend a result by J. Busca in a sense of domains, and we present a simple proof based on local maximum principle by Gilbarg and Trudinger with iterations.

• Journal of the Korean Mathematical Society
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• 제53권3호
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• pp.533-547
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• 2016

We prove an Omori-Yau maximum principle on Alexandrov spaces which do not have Perelman singular points and satisfy the infinitesimal Bishop-Gromov condition.

• Journal of Environmental Impact Assessment
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• 제13권4호
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• pp.213-222
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• 2004

Exergy is defined as the amount of work (entropy-free energy) a system can perform when it is brought into thermodynamic equilibrium with its environment. Exergy measures the distance from the inorganic soup in energy terms. Therefore, exergy can be considered as fuel for any system that converts energy and matter in a metabolic process. The aim of this study is to introduce structural dynamic modelling which is based on maximum exergy principle. Especially, almost ecological models couldn't explain algal succession until now. New model (structural dynamic model) is anticipated to predict or explain the succession theory. If the new concept using maximum exergy principle is used, algal succession can be explained in many actual cases. Therefore, It is estimated that structural dynamic model using maximum exergy principle might be a excellent tool to understand succession of nature from now on.

• Bulletin of the Korean Mathematical Society
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• 제51권2호
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• pp.567-577
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• 2014

In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form $\mathbb{M}^{n+1}(c)$ (c = 1, 0,-1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in $\mathbb{S}^{n+1}(1)$ with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 한국정밀공학회 2007년도 추계학술대회 논문집
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• pp.571-572
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• 2007

• The Transactions of the Korean Institute of Electrical Engineers
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• 제34권8호
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• pp.308-316
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• 1985

This paper proposes an analytic tool for long-term generation expansion planning based on the maximum principle. Many research works have been performed in the field of generation expansion planning. But few works can be found with the maxinmum principle. A recently published one worked by professor Young Moon Park et al. shows remarkable improvements in modeling and computation. But this modeling allows only thermal units. This paper has extended Professor Park's model so that the optimal pumped-storage operation is taken into account. So the ability for practical application is enhanced. In addition, the analytic supply-shortage cost function is included. The maximum principle is solved by gradient search due to its simplicity. Every iteration is treated as if mathematical programming such that all controls from the initial to the terminal time are manipulated within the same plane. Proposed methodology is tested in a real scale power system and the simulation results are compared with other available package. Capability of proposed method is fully demonstrated. It is expected that the proposed method can be served as a powerful analytic tool for long-term generation expansion planning.

• Journal of the Korean Institute of Telematics and Electronics
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• 제11권3호
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• pp.27-31
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• 1974

The maximum principle of Pontryagin provides the celebrated method to obtain the optimum control switching time and switching points on the nuclear reactor. The control trajectories transfered from its initial state to the target state are optimized based on time optioptimal control method with the given reactor parameters and the piecewise constant input values.

• Journal of the Korean Mathematical Society
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• 제58권4호
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• pp.1001-1017
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• 2021

In this paper, we first apply parabolic inequalities and a maximum principle to give a new proof for symmetry and monotonicity of solutions to fractional elliptic equations with gradient term by the method of moving planes. Under the condition of suitable initial value, by maximum principles for the fractional parabolic equations, we obtain symmetry and monotonicity of positive solutions for each finite time to nonlinear fractional parabolic equations in a bounded domain and the whole space. More generally, if bounded domain is a ball, then we show that the solution is radially symmetric and monotone decreasing about the origin for each finite time. We firmly believe that parabolic inequalities and a maximum principle introduced here can be conveniently applied to study a variety of nonlocal elliptic and parabolic problems with more general operators and more general nonlinearities.