• 대한수학회지
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• 제47권4호
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• pp.743-766
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• 2010

We study the existence of weak solution for the stationary Nordstr$\ddot{o}$m-Vlasov equations in a bounded domain. The proof follows by fixed point method. The asymptotic behavior for large light speed is analyzed as well. We justify the convergence towards the stationary Vlasov-Poisson model for stellar dynamics.

• 대한수학회지
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• 제33권2호
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• pp.399-411
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• 1996

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^n$ and let $A(\Omega)$ denote the functions holomorphic on $\Omega$ and continuous on $\bar{\Omega}$. A point $p \in b\Omega$ is a peak point if there is a function $f \in A(\Omega)$ such that $f(p) = 1, and $\mid$f(z)$\mid$ < 1 for z \in \bar{\Omega} - {p}$.

• 대한수학회지
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• 제33권2호
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• pp.333-346
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• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• 대한수학회지
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• 제37권1호
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• pp.85-109
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• 2000

In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form (equation omitted) will be discussed. Here $\Omega$ is a smooth and bounded domain in $R^{n}$ (n $\geq$ 1), f(x,u) = │u│$^{\alpha}$/sgn(u)-h(x), 0 < $\alpha$ < 1, (n $\geq$ 1) and h is a ${\gamma}$- Holder continuous function on $\Omega$ for some 0 < ${\gamma}$ < 1.a}$ < 1.

• 대한수학회보
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• 제51권6호
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• 대한수학회보
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• 제57권4호
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• pp.921-932
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• 2020

In this paper we prove the local existence of strong solutions to an isentropic compressible Navier-Stokes-P1 approximate model arising in radiation hydrodynamics in a bounded domain with vacuum.

• 대한수학회보
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• 제38권2호
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• pp.325-336
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• 2001

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a quadratic function equation f(x+y+z)+f(x-y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam-Rassias stability of the equation on bounded domain.

• 대한수학회보
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• 제54권4호
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• pp.1457-1470
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• 2017

In this paper, we consider the stabilization of the viscoelastic wave equation with variable coefficients in a bounded domain with smooth boundary, subject to linear dissipative internal feedback with a delay. Our stabilization result is mainly based on the use of the Riemannian geometry methods and Lyapunov functional techniques.

• 대한수학회보
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• 제57권2호
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• pp.281-294
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• 2020

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.309-322
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• 2008

We prove the existence of infinitely many solutions of the nonlinear higher order elliptic equation with Dirichlet boundary condition $(-{\Delta})^mu=q(x,u)$ in ${\Omega}$, where $m{\geq}1$ is an integer and ${\Omega}{\subset}{R^n}$ is a bounded domain with smooth boundary, when q(x,u) satisfies some conditions.