• 대한수학회논문집
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• 제36권3호
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• pp.527-548
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• 2021

In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

• 대한수학회논문집
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• 제32권3호
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• East Asian mathematical journal
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• 제38권1호
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• pp.21-31
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• 2022

This paper is concerned with the optimal control problem associated to the self-organizing target detection model in 1D domains. That is, we show the global existence of weak solution and the existence of optimal control.

• 대한수학회논문집
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• 제14권2호
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• pp.301-310
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• 1999

This paper is concerned with the existence of positive solution of a semilinear elliptic equation with homogeneous Dirichlet boundary condition.

• 대한수학회보
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• 제43권3호
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• pp.599-610
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• 2006

The aim of this paper is to give an existence theorem for a strong solution of generalized vector quasi-equilibrium problems of the weak type II due to Hou et al. using the equilibrium existence theorem for 1-person game, and as an application, we shall give a generalized quasivariational inequality.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.15-23
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• 2001

This paper gives the sufficient conditions for the existence of positive solution of a quasilinear elliptic with homogeneous Dirichlet boundary conditon.

• East Asian mathematical journal
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• 제35권5호
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• pp.535-545
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• 2019

This paper is concerned with the optimal control problem associated to strong solution of Belousov-Zhabotinskii reaction model in 2D domain. That is, we otain the global existence of strong solution and show the existence of optimal control.

• 대한수학회보
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• 제55권2호
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• pp.591-598
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• 2018

This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.51-64
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• 1996

In this paper we investigate the existence of weak solutions of a nonlinear beam equation under Dirichlet boundary condition on the interval $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and periodic condition on the variable $t$, $u_{tt}+u_{xxxx}=p(x,t,u)$. We show that if $p$ satisfies condition $(p_1)-(p_3)$, then the nonlinear beam equation possesses at least one weak solution.

• 한국마린엔지니어링학회:학술대회논문집
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• 한국마린엔지니어링학회 2001년도 춘계학술대회 논문집
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• pp.95-99
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• 2001

As a way to use energy effectively, the present study is aimed at investigating the performance characteristics of a Single Effect LiBr/Water Absorption Refrigerator using a low temperature driving heat-source. It was carried out by changing the driving heat-source temperature, the cold water outlet temperature(the refrigeration load), the cooling water inlet temperature, and the weak solution flow rate and this study compares the performance characteristics of refrigerator against the existence and non-existence of the Recirculation of the Weak solution which is used as a method to improve the performance of refrigerator. In case of Recirculation of the weak solution, more improved the Refrigeration Capacity and COP was obtained, and these effects became more larger in the high temperature of driving heat-source and large quantity of solution.