• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.547-554
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• 2014

In this paper, we consider the existence and uniqueness of global weak solution for a sixth-order classical surface-diffusion equation in one spatial dimension. Moreover, the regularity and blow-up of solutions are also studied.

• Asian review of World Histories
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• v.3 no.1
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• pp.113-135
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• 2015

The word 'urbanity' literally means 'quality or state of being urban' where the criterion of urban economic and civic culture is assumed despite the general celebration of cultural uniqueness of urban centers. The narratives celebrating the uniqueness of urban centers since the ancient past till recent times could not get rid of the broad categorization of the urban models depending on their contextual networks of trade, mobility and culture. This paper attempts to explore whether the urban cultures in South Asia even preceding a global phenomenon like colonialism were actually reflecting an idea of urbanity where the urban culture, including planning and architecture reflected a trans-national model. This paper particularly concentrates on the medieval period when a pattern of urbanity took shape in this subcontinent under the influence of Islam, which could be explained by its particular idea of urban model, cultural exchange and vibrant trade networks.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.77-90
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• 2004

The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system of the Dirichlet problem on the bounded domain ${\Omega}$ in $R^n$. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. This result yields an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.447-463
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• 2021

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.93-102
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• 2004

A model of three trophic level food chain with ratio dependence is considered. The existencem uniqueness and stability of its solutions are investigated.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1599-1619
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• 2018

In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity c tends to infinity in a pointwise sense.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.35-64
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• 2021

In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.1
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• pp.99-112
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• 1994

This paper describe the development of a systematic method of slicing solid parts based on a data structure called Sliced Profile Data Structure(SPDS). SPDS is an augmented polygon data structure that allows multiple layers of sliced profiles to be connected together. The method consists of five steps: (1) Selection of slicing directions, (2) Determination of slicing levels, (3) Creation of sliced profiles, (4) Connection of sliced profiles, and (5) Refinement. The presented method is aimed at enhancing the applicability of CSG for manufacturing by overcoming the problem of non-uniqueness and global nature. The SPDS-based method of feature extraction is suitable for recognizing broad scope of features with detailed information. The method is also suitable for identifying the global relationships among features and is capable of incorporating the context dependency of feature extraction.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.189-206
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• 2014

In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation $$u_{tt}-M({\parallel}{\nabla}u{\parallel}^2){\triangle}u+{\alpha}u_t+f(u)=0\;in\;{\Omega}{\times}[0,{\infty}),\\u(x,t)=0\;on\;{\Gamma}_1{\times}[0,{\infty}),\\{\frac{{\partial}u}{\partial{\nu}}}+g(u_t)=0\;on\;{\Gamma}_0{\times}[0,{\infty}),\\u(x,0)=u_0,u_t(x,0)=u_1\;in\;{\Omega}$$ with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. [33]. Furthermore,we overcome some difficulties due to the presence of nonlinear terms $M({\parallel}{\nabla}u{\parallel}^2)$ and $g(u_t)$ by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.379-403
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• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.