摘要本文研究了一类非线性抛物型微分系统的奇异摄动问题.首先利用奇异摄动方法构造了外部解.其次,分别采用多尺度法和伸长变量法获得尖层校正项、边界层校正项和初始层校正项.最后得到了广义解的渐近展开解.利用不动点定理证明了渐近解的一致有效性.该渐近解可用于对广义解进行解析运算,可以了解其更多的特征,因此具有较好的应用前景. | | 服务 | | ![](http://123.57.41.99/jweb_yysxxb/images/arrow.jpg) | 加入引用管理器 | ![](http://123.57.41.99/jweb_yysxxb/images/arrow.jpg) | E-mail Alert | ![](http://123.57.41.99/jweb_yysxxb/images/arrow.jpg) | RSS | 收稿日期: 2019-04-16 | | 基金资助:国家自然科学基金(11271247),安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016520),安徽省教育厅自然科学重点基金项目(KJ2015A347,KJ2017A702,KJ2019A1300),安徽省教育厅重点教研项目(2018jyxm0594,2016jyxm0677,2017jyxm0591),亳州学院重点教学研究项目(2017zdjy02)和亳州学院重点科学研究项目(BYZ2017B02,BYZ2017B03)资助. |
[1] | De Jager, E M, Jiang F R. The Theory of Singular Perturbation. Amsterdam:North-Holland Publishing Co., 1996 | [2] | Barbu L, Morosanu G. Singularly Perturbed Boundary-Value Problems. Basel:Birkhauserm Verlag AG, 2007 | [3] | Constantin A. On the existence of positive solutions of second order differential equations. Ann. Mat. Pura. Appl., 2005, 184(4):131-138 | [4] | Ertem T, Zafer A. Monotone positive solutions for a class of second-order nonlinear differential equations. J. Comput. Appl. Math., 2014, 259:672-681 | [5] | Hovhannisyan G, Vulanovic R. Stability inequalities for one-dimensional singular perturbation problems. Nonlinear Stud., 2008, 15(4):297-322 | [6] | Graef J R, Kong L. Solutions of second order multi-point boundary value problems. Math. Proc. Camb. Philos. Soc., 2008, 145(2):489-510 | [7] | Barbu L, Cosma E. Elliptic regularizations for the nonlinear heat equation. J. Math. Anal. Appl., 2009, 351(2):392-399 | [8] | Martinez S, Wolanskin. A singular perturbation problem for a quasi-linear operator satisfying the natural condition of Lieberman. SIAM J. Math. Anal., 2009, 41(1):318-359 | [9] | Kellogg R B, Koptev N A. Singularly perturbed semilinear reaction-diffusion problem in a polygonal domain. J. Differ. Equations, 2010, 248(1):184-208 | [10] | Bonfoh A, Grassrlli M, Miranville A. Intertial manifolds for a singular perturbation of the viscous Cahn-Hilliiard-Gurtin equation. Topol. Methods Nonlinear Anal., 2010, 35(1):155-185 | [11] | Faye L, Frenod E, Seck D. Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment. Discrete Contin. Dyn. Syst., 2011, 29(3):1001-1030 | [12] | Tian C R, Zhu P. Existence and asymptotic behavior of solutions for quasilinear parabolic systems. Acta Appl. Math., 2012, 121(1):157-173 | [13] | Skrynnikox Y. Solving initial value problem by matching asymptotic expansions. SIAM J. Appl. Math., 2012, 72(1):405-416 | [14] | Samusenko P F. Asymptotic integration of degenerate singularly perturbed systems of parabolic partial differential equations. J. Math. Sci., New York, 2013, 189(5):834-847 | [15] | Mo J Q. Singular perturbation for a class of nonlinear reaction diffusion systems. Science in China, Ser A., 1989, 32(11):1306-1315 | [16] | Mo J Q, Lin W T. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations. J. Sys. Sci. & Complexity, 2008, 20(1):119-128 | [17] | Mo J Q. A class of singulaely perturbed differential-difference reaction diffusion equations. Adv. Math., 2009, 38(2):227-230 | [18] | Mo J Q. Approximate solution of homotopic mapping to solitary for generalized nonlinear KdV system. Chin. Phys. Lett., 2009, 26(1):010204 | [19] | Mo J Q. A variational iteration solving method for a class of generalized Boussinesq equations. Chin. Phys. Lett., 2009, 26(6):060202 | [20] | Mo J Q. Homotopic mapping solving method for gain fluency of laser pulse amplifier. Science in China, Ser. G, 2009, 39(5):568-661 | [21] | Mo J Q, Lin W T. Asymptotic solution for a class of sea-air oscillator model for El-Nino-southern oscillation. Chin. Phys., 2008, 17(2):370-372 | [22] | Mo J Q. A class of homotopic solving method for ENSO mpdel. Acta Math. Sci., 2009, 29(1):101-109 | [23] | Mo J Q, Chen H J. The corner layer solution of Robin problem for semilinear equation. Math. Appl., 2012, 25(1):1-4 | [24] | Mo J Q, Lin Y H, Lin W T, Chen L H. Perturbed solving method for interdecadal sea-air oscillator model. Chin. Geographical Sci., 2012, 22(1):42-47 | [25] | Feng Y H, Mo J Q. Asymptotic solution for singularly perturbed fractional order differential equation. J. Math., 2016, 36(2):239-245 | [26] | Feng Y H, Chen X F, Mo J Q. The shock wave solution of a class of singularly perturbed problem for generalized nonlinear reaction diffusion equation. Math. Appl., 2017, 30(1):1-7 | [27] | 冯依虎, 莫嘉琪. 一类非线性非局部扰动LGH方程的孤子行波解. 应用数学和力学, 2016, 37(4):426-433(Feng Y H, Mo J Q. A class of soliton travelling wave solution for the nonlinear nonlocal disturbed LGH equation. Appl. Math. Mech., 2016, 37(4):426-433) | [28] | 冯依虎, 史兰芳, 莫嘉琪. 关于将飞秒脉冲激光用于纳米金属薄膜传导系统的研究. 工程数学学报, 2017, 34(1):13-20(Feng Y H, Shi L F, Mo J Q. Study of transfers system for femtosecond pulse laser to Nano metal film. Chin. J. Engin. Math., 2017, 34(1):13-20) | [29] | 冯依虎, 陈怀军, 莫嘉琪. 激光脉冲放大器增益通量耦合系统解. 应用数学和力学, 2017, 38(5):561-569(Feng Y H, Chen H J, Mo J Q. Asymptotic solution to a class of nonlinear singular perturbation autonomic differential system. Appl. Math. Mech., 2017, 38(5):561-569) | [30] | 冯依虎, 莫嘉琪. 一类广义奇摄动非线性双曲型积分-微分方程模型. 吉林大学学报(理学版), 2017, 55(5):1055-1060(Feng Y H, Mo J Q. A class of generalized singularly perturbed nonlinear hyperbolic integraldifferential equation model. J. Jilin Univ., 2017, 55(5):1055-1060) |
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