• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.319-330
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• 2018

This paper is concerned with the global asymptotic stability of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The discussion is based on analytic semigroups theory and the gradually regularization method. The results obtained in this paper improve and extend some related conclusions on this topic.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.405-417
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• 2005

In this paper, the oscillation and asymptotic stability behavior of a third order linear impulsive equation are investigated. A lemma is presented to deal with the sign relation of the nonoscillatory solutions and their derived functions. By the lemma explicit sufficient conditions are obtained for all solutions either oscillating or asymptotically tending to zero. Two illustrative examples are proposed to demonstrate the effectiveness of the conditions.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.37-51
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• 2004

In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $\Delta[x(n)-\sumpi(n)x(n-k_i)]+\sumqj(n)f(x(n-\iota_j))=r(n)$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.259-267
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• 2013

We present a high-order potential flow model for the motion of hydrodynamic unstable interfaces in cylindrical geometry. The asymptotic solutions of the bubbles in the gravity-induced instability and the shock-induced instability are obtained from the high-order model. We show that the model gives significant high-order corrections for the solution of the bubble.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.555-565
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• 2008

We will derive the asymptotic expansions of solutions of the heat equation with hyperfunctions initial data.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.47-62
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• 1997

This paper is concerned with investigating the global as-ymptotic behavior of the zero solution of the initial-boundary value problem for a nonlinear fourth order wave equation, Moreover an esti-mate of the rate of decay of the solutions is obtained.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.431-447
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• 2011

We investigate the asymptotic behavior of positive solutions to the elliptic equation (0.1) ${\Delta}u+|x|^{l_1}u^p+|x|^{l_2}u^q=0$ in $\mathbb{R}^n$. We obtain a conclusion that, for n $\geq$ 3, -2 < $l_2$ < $l_1$ $\leq$ 0 and q > p > 1, any positive radial solution to (0.1) has the following properties: $lim_{r{\rightarrow}{\infty}}r^{\frac{2+l_1}{p-1}}\;u$ and $lim_{r{\rightarrow}0}r^{\frac{2+l_2}{q-1}}\;u$ always exist if $\frac{n+1_1}{n-2}$ < p < q, $p\;{\neq}\;\frac{n+2+2l_1}{n-2}$, $q\;{\neq}\;\frac{n+2+2l_2}{n-2}$. In addition, we prove that the singular positive solution of (0.1) is unique under some conditions.

• Journal of Biomedical Engineering Research
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• v.5 no.1
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• pp.9-14
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• 1984

The asymptotic solution using the Tailor series has been given explicit form for the solute concentration and overall solute removal in hemodiafilter using one dimensional model. The numerical solutions have been calculated within 0.001% error by the Romberg integration method. Compared with the numerical solutions, the oneterm asymptotic solutions were found to be within 3% error for the condition > 3.0 and three-terms asymtotic solutions were required for the condition >0.7 where denotes measure of convection over diffusional transport and a the ratio of blood flow rate over dialysate flow rate.