Generalized quazilinearization for systems of degenerate singular perturbation problems

Ahmed R. Abd-Ellateef Kamar; Tadeusz Jankowski

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Generalized quazilinearization for systems of degenerate singular perturbation problems

机译：退化奇异摄动问题系统的广义拟线性化

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摘要

In this paper, we extend the method of generalized quasilinearization to systems of degenerate singular perturbation problems. We construct, under suitable conditions, monotone sequences of lower and upper approximate solutions which converge uniformly and quadratically to the unique solution of the system of degenerate singular perturbation problems.

机译：在本文中，我们将广义拟线性化方法扩展到退化奇异摄动问题系统。在适当的条件下，我们构造了上下近似解的单调序列，它们均匀并二次收敛于退化奇异摄动问题系统的唯一解。

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《Nonlinear studies》 |2013年第2期|共7页
作者
Ahmed R. Abd-Ellateef Kamar; Tadeusz Jankowski;
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正文语种 eng
中图分类高等数学;
关键词
Generalized quazilinearization; degenerate singular perturbation problem;

机译：广义拟线性化;退化奇异摄动问题;

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专利

1. Generalized quazilinearization for systems of degenerate singular perturbation problems [J] . Ahmed R. Abd-Ellateef Kamar, Tadeusz Jankowski Nonlinear studies . 2013,第2期

机译：退化奇异摄动问题系统的广义拟线性化
2. Limit-point criteria for semi-degenerate singular Hamiltonian differential systems with perturbation terms [J] . Qi JG Journal of Mathematical Analysis and Applications . 2007,第2期

机译：具有摄动项的半退化奇异哈密顿微分系统的极限点准则
3. Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation [J] . Guoping Lu, Ho D.W.C. IEEE Transactions on Automatic Control . 2006,第5期

机译：具有非线性摄动的连续时间奇异系统的广义二次稳定性
4. Global Classical Discontinuous Solutions to the Generalized Riemann Problem for Linearly Degenerate Hyperbolic Conservation Laws under Small BV Perturbations of the Initial Data [C] . Zhi-Qiang Shao International Conference on Hyperbolic Problems . 2012

机译：在初始数据的小型BV扰动下线性退化双曲保守法的全局古典不连续解决方案
5. Invariant measures for degenerate random perturbations of discrete-time dynamical systems. [D] . Yarmola, Tatiana. 2008

机译：离散时间动力系统退化简并随机扰动的不变测度。
6. Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels [O] . A. SINGER, D. GILLESPIE, J. NORBURY, -1

机译：稳态泊松－能斯特－普朗克系统的奇异摄动分析：在离子通道中的应用
7. Limit-point criteria for semi-degenerate singular Hamiltonian differential systems with perturbation terms [O] . Qi Jiangang 2007

机译：具有摄动项的半退化奇异哈密顿微分系统的极限点准则

Generalized quazilinearization for systems of degenerate singular perturbation problems

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