• 제목/요약/키워드: Asymptotic behavior

검색결과 267건 처리시간 0.027초

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO 3D CONVECTIVE BRINKMAN-FORCHHEIMER EQUATIONS WITH FINITE DELAYS

  • Le, Thi Thuy
    • 대한수학회논문집
    • /
    • 제36권3호
    • /
    • pp.527-548
    • /
    • 2021
  • In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

ON EXISTENCE OF SOLUTIONS OF DEGENERATE WAVE EQUATIONS WITH NONLINEAR DAMPING TERMS

  • Park, Jong-Yeoul;Bae, Jeong-Ja
    • 대한수학회지
    • /
    • 제35권2호
    • /
    • pp.465-490
    • /
    • 1998
  • In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) + ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)+$\delta$$u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) + ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)+$\delta$$v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.

  • PDF

Nonlinear static analysis of composite cylinders with metamaterial core layer, adjustable Poisson's ratio, and non-uniform thickness

  • Eipakchi, Hamidreza;Nasrekani, Farid Mahboubi
    • Steel and Composite Structures
    • /
    • 제43권2호
    • /
    • pp.241-256
    • /
    • 2022
  • In this article, an analytical procedure is presented for static analysis of composite cylinders with the geometrically nonlinear behavior, and non-uniform thickness profiles under different loading conditions by considering moderately large deformation. The composite cylinder includes two inner and outer isotropic layers and one honeycomb core layer with adjustable Poisson's ratio. The Mirsky-Herman theory in conjunction with the von-Karman nonlinear theory is employed to extract the governing equations which are a system of nonlinear differential equations with variable coefficients. The governing equations are solved analytically using the matched asymptotic expansion (MAE) method of the perturbation technique and the effects of moderately large deformations are studied. The presented method obtains the results with fast convergence and high accuracy even in the regions near the boundaries. Highlights: • An analytical procedure based on the matched asymptotic expansion method is proposed for the static nonlinear analysis of composite cylindrical shells with a honeycomb core layer and non-uniform thickness. • The effect of moderately large deformation has been considered in the kinematic relations by assuming the nonlinear von Karman theory. • By conducting a parametric study, the effect of the honeycomb structure on the results is studied. • By adjusting the Poisson ratio, the effect of auxetic behavior on the nonlinear results is investigated.

WELL-POSEDNESS AND ASYMPTOTIC BEHAVIOR OF PARTLY DISSIPATIVE REACTION DIFFUSION SYSTEMS WITH MEMORY

  • Vu Trong Luong;Nguyen Duong Toan
    • 대한수학회보
    • /
    • 제61권1호
    • /
    • pp.161-193
    • /
    • 2024
  • In this paper, we consider the asymptotic behavior of solutions for the partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type with hereditary memory and a very large class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. We first prove the existence and uniqueness of weak solutions to the initial boundary value problem for the above-mentioned model. Next, we investigate the existence of a uniform attractor of this problem, where the time-dependent forcing term h ∈ L2b(ℝ; H-1(ℝN)) is the only translation bounded instead of translation compact. Finally, we prove the regularity of the uniform attractor A, i.e., A is a bounded subset of H2(ℝN) × H1(ℝN) × L2µ(ℝ+, H2(ℝN)). The results in this paper will extend and improve some previously obtained results, which have not been studied before in the case of non-autonomous, exponential growth nonlinearity and contain memory kernels.

A NON-ASYMPTOTIC METHOD FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS

  • File, Gemechis;Reddy, Y.N.
    • Journal of applied mathematics & informatics
    • /
    • 제32권1_2호
    • /
    • pp.39-53
    • /
    • 2014
  • In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

점근해법에 의한 열자격 전류식의 분석 (The Analysis of TSC Equation by Asymptotic Estimation)

  • 오용철;홍진웅;김기준
    • 한국전기전자재료학회:학술대회논문집
    • /
    • 한국전기전자재료학회 2003년도 제5회 학술대회 논문집 일렉트렛트 및 응용기술연구회
    • /
    • pp.96-99
    • /
    • 2003
  • In this paper, it presents a method to calculate the escape frequency factor$(\nu)$ and its verification from TSC(Thermally Stimulated Current) equation and their simulation curves. To apply calculation method of $\nu$ using asymptotic estimation, it utilized TSC data with 1K interval. This method enables one to get the exact value of $\nu$ and activation energy at the same time by using computer programming. So, it regards their calculation method as a useful process to obtain the value of physical behavior.

  • PDF

Comparison of the Kaplan-Meier and Nelson Estimators using Bootstrap Confidence Intervals

  • Cha, Young Joon;Lee, Jae Man
    • 품질경영학회지
    • /
    • 제23권4호
    • /
    • pp.42-51
    • /
    • 1995
  • The bootstrap confidence intervals are a computer-based method for assigning measures of accuracy to statistical estimators. In this paper we examine the small sample behavior of the Kaplan-Meier and Nelson-type estimators for the survival function using the bootstrap and asymptotic normal-theory confidence intervals. The Nelson-type estimator is nearly always better than the Kaplan-Meier estimator in the sense of achieved error rates. From the point of confidence length, the reverse is true. Also, we show that the bootstrap confidence intervals are better than the asymptotic normal-theory confidence intervals in terms of achieved error rates and confidence length.

  • PDF

Nonparametric Tests for Monotonicity Properties of Mean Residual Life Function

  • Jeon, Jong-Woo;Park, Dong-Ho
    • Journal of the Korean Statistical Society
    • /
    • 제26권1호
    • /
    • pp.101-116
    • /
    • 1997
  • This is primarily an expository paper that presents several nonparametric procedures for testing exponentiality against certain monotonicity properties of the mean residual life function, tests against the trend change in such function attract a great deal of attention of late in reliability analysis. In this note, we present some of the known testing procedures regarding the behavior of mean residual life function. These tests are also compared in terms of asymptotic relative efficiency and empirical power against a few alternatives. The tests based on incomplete data are also briefly discussed.

  • PDF

A Goodness of Fit Approach for Testing NBUFR (NWUFR) and NBAFR (NWAFR) Properties

  • Mahmoud, M.A.W.;Alim, N.A. Abdul
    • International Journal of Reliability and Applications
    • /
    • 제9권2호
    • /
    • pp.125-140
    • /
    • 2008
  • The new better than used failure rate (NBUFR), Abouammoh and Ahmed (1988), and new better than average failure rate (NBAFR) Loh (1984) classes of life distributions, have been considered in the literature as natural weakenings of NBU (NWU) property. The paper considers testing exponentiality against strictly NBUFR (NBAFR) alternatives, or their duals, based on goodness of fit approach that is possible in life testing problems and that it results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. The asymptotic normality are proved. Powers, Pitman asymptotic efficiency and critical points are computed. Dealing with censored data case also studied. Practical applications of our tests in the medical sciences are present.

  • PDF