• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.625-637
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• 2010

In this paper, we are concerned with the quasilinear elliptic systems with boundary blow-up conditions in a smooth bounded domain. Using the method of lower and upper solutions, we prove the sufficient conditions for the existence of the positive solution. Our main results are new and extend the results in [Mingxin Wang, Lei Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Analysis(In Press)].

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.235-242
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• 2012

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.2
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• pp.85-91
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Gannesh C. Gorain [1]. Energy decay rates are obtained by the exponential stability of solutions by using multiplier technique.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.151-157
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• 1992

The objective of this paper is to study two dimensional waves on the interface between two immiscible, invicid and incompressible fluid bounded by two rigid varing boundaries when gravity and surface tension appear. By using unfied asymptotic method, a K-dV equation with higher order terms from which many model equations for the fluid domain can be obtained, is derived.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.633-637
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• 2009

We prove using the Szeg$\H{o}$ kernel and the Garabedian kernel that a Toeplitz operator on the boundary of $C^{\infty}$ smoothly bounded domain associated to a smooth symbol vanishes only when the symbol vanishes identically. This gives a generalization of previous results on the unit disk to more general domains in the plane.

• East Asian mathematical journal
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• v.28 no.3
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• pp.339-345
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• 2012

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchho type wave equation with acoustic boundary in a bounded domain in $R^n$. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.65-70
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• 2007

We study the existence of nontrivial solutions of the Gradient type Dirichlet boundary value problem for elliptic systems of the form $-{\Delta}U(x)={\nabla}F(x,U(x)),x{\in}{\Omega}$, where ${\Omega}{\subset}R^N(N{\geq}1)$ is a bounded regular domain and U = (u, v) : ${\Omega}{\rightarrow}R^2$. To study the system we use the liking theorem on product space.

• East Asian mathematical journal
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• v.30 no.3
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• pp.249-258
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• 2014

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang[14]. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.97-101
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• 1995

In [6], the author studied the property of the Szeg kernel and had a result that if $\Omega$ is a smoothly bounded domain in C and the Szeg kernel associated with $\Omega$ is rational, then any proper holomorphic map from $\Omega$ to the unit disc U is rational. It leads to the study of the proper rational map of $\Omega$ to U. In this note, first we simplify the proof of the above result and prove an existence theorem of a proper rational map. Before we proceed to state our result, we must recall some preliminary facts.(omitted)

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1773-1778
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• 2006

Steady-state natural convection heat transfer characteristics from cylinders in a multiply-connected bounded region are clarified. A spectral finite difference scheme (spectral decomposition of the system of partial differential equations, semi-implicit time integration) is applied in numerical analysis, with a boundary-fitted conformal coordinate system through a Jacobian elliptic function with a successive transformation to formulate a system of governing equations in terms of a stream function, vorticity and temperature. Multiplicity of the domain is expressed explicitly.