• Korean Journal of Mathematics
• /
• v.26 no.4
• /
• pp.747-756
• /
• 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 Society of Visualization
• /
• v.19 no.2
• /
• pp.15-25
• /
• 2021

Numerical studies on the hydrodynamics of a freely falling rigid sphere in bounded and unbounded water domains are presented having investigation on the drag coefficient, normalized velocity, surface pressure and skin friction coefficient as a function of time. Two different conditions of the bounded and unbounded domains have been simulated by setting the blockage ratio. Four cases of bounded domains (B.R. = 1%, 25%, 45%, 55%, 65% and 75%) have been taken, whereas the unbounded domain has been considered with 0.01%. In the case of the bounded domain (higher values of B.R.), a substantial reduction in normalized velocity and increase in the drag coefficient have been found in presence of the bounded domain. Moreover, bounded domains also yield a significant increase in the pressure coefficient when the sphere is partially submerged, but the insignificant effect is found on the skin friction coefficient. In the case of the unbounded domain, a significant reduction in normalized velocity occurs with a decrease in Reynolds number (Re) and also increase in the drag coefficient.

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.13-19
• /
• 2016

In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1221-1241
• /
• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.135-146
• /
• 1997

For the numerical simulation of wave phenomena either in unbounded domains that it is not feasible to compute solutions on the entire region, it is needed to truncate the original domains to manageable bounded domains whose geometries are simple but usually nonsmooth. On the artificial boundaries thus created, absorbing boundary conditions are taken so that the significant part of waves arriving at the artificial boundaries can be transmitted [5,10,11,16,17,26]$.

• Journal of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.125-137
• /
• 2000

In the present paper, the classical results of the stability of isometries obtained by some authors will be generalized; More precisely, the stability of isometries on restricted (unbounded or bounded) domains will be investigated.

• Communications of the Korean Mathematical Society
• /
• v.20 no.4
• /
• pp.731-749
• /
• 2005

In this paper, we study the two dimensional g-Navier­Stokes equations on some unbounded domain ${\Omega}\;{\subset}\;R^2$. We prove the existence of the global attractor for the two dimensional g-Navier­Stokes equations under suitable conditions. Also, we estimate the dimension of the global attractor. For this purpose, we exploit the concept of asymptotic compactness used by Rosa for the usual Navier-Stokes equations.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.423-443
• /
• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• Earthquakes and Structures
• /
• v.3 no.3_4
• /
• pp.383-411
• /
• 2012

The objective of the present paper is to review and implement the most recent developments in the Spectral Element Method (SEM), as well as improve aspects of its implementation in the study of wave propagation by numerical simulation in elastic unbounded domains. The classical formulation of the method is reviewed, and the construction of the mass matrix, stiffness matrix and the external force vector is expressed in terms of matrix operations that are familiar to earthquake engineers. To account for the radiation condition at the external boundaries of the domain, a new absorbing boundary condition, based on the Perfectly Matched Layer (PML) is proposed and implemented. The new formulation, referred to as the Multi-Axial Perfectly Matched Layer (M-PML), results from generalizing the classical Perfectly Matched Layer to a medium in which damping profiles are specified in more than one direction.

• Journal of Korean Association for Spatial Structures
• /
• v.6 no.2 s.20
• /
• pp.13-19
• /
• 2006