• 충청수학회지
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• 제4권1호
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• pp.115-119
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• 1991

In this paper we obtain the asymptotic behavior of solutions of the perturbed system x' = (A(t) + B(t))x of x' = A(t)x by using the Floquet theorem.

• East Asian mathematical journal
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• 제13권2호
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• pp.283-292
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• 1997

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.156-162
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• 1998

The main objective of this paper is to study the boundedness of solutions of the differential equation $L_{n} {\chi}＋F(t,{\chi}) = f(t), n {\geq} 2 $(*) Necessary and sufficient conditions for boundedness of all solutions of (*) will be obtainded. The asymptotic behavior of solutions of (*) will also be studied.

• 대한수학회지
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• 제35권4호
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• pp.1019-1043
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• 1998

In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions ( $u_{\in}$, $A_{\in}$) which minimize the Ginzburg-Landau energy functional $E_{\in}$(u, A). We show that the solutions ( $u_{\in$}$ , $A_{\in}$) converge to some ( $u_{*}$, $A_{*}$) in various norms as the coupling parameter $\in$longrightarrow0.ow0.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.217-230
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• 2017

In this paper we deal with the difference equation $$y_{n+1}=\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d}$$, $$n{\in}\mathbb{N}_0$$, where the coefficients a, b, c, d are positive real numbers and the initial conditions $y_{-2}$, $y_{-1}$, $y_0$ are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

• 대한수학회보
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• 제44권3호
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• pp.547-567
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• 2007

We obtain spatial-temporal decay rates of weak solutions of incompressible flows in exterior domains. When a domain has a boundary, the pressure term yields difficulties since we do not have enough information on the pressure term near the boundary. For our calculations we provide an idea which does not require any pressure information. We also estimated the spatial and temporal asymptotic behavior for strong solutions.

• 대한수학회보
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• 제52권4호
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• pp.1059-1068
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• 2015

The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

• 한국지반공학회논문집
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• 제21권6호
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• pp.93-100
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• 2005

수압파쇄시 다중으로 분할된 균열의 생성은 자주 발생되는 현상이며 이러한 균열군은 단균열과는 달리 상당히 다른 거동을 나타낸다. 그러나 대부분의 수치기법으로는 이러한 균열군 거동의 모사는 계산량의 증가로 결코 쉽지 않다. 따라서 본 논문에서는 수압파쇄시 생성되는 다수의 균열 변위를 경계병치법을 사용하여 효과적으로 계산하기 위한 방법을 제시하였다. 우선 평행하면서 아주 가깝게 위치한 다중 분할 균열의 점근적 해를 구하고 경계병치법의 균열에 사용된 병치점의 수를 변화시켜 점근적 해와 비교하였다. 그 결과 기존의 기준에 비해 병치점의 수를 10배정도 줄이더라도 얻어지는 결과에는 별 차이가 없음을 밝혀냈다. 따라서 이보다 더욱 복잡한 균열이 존재하는 실제의 경우 병치점의 수를 줄여 적용하여도 경계병치법에 의한 계산은 유효하다는 결론을 얻었다.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• 대한수학회논문집
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• 제36권3호
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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.