A Class of Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations With Boundary Perturbation
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摘要: 研究了一类具有边界摄动的非线性非局部反应扩散方程奇摄动Robin初始边值问题．在适当的条件下，首先求出了原问题的外部解，然后利用伸长变量、合成展开法和幂级数展开理论构造出解的初始层项，并由此得到解的形式渐近展开式．最后利用微分不等式理论，讨论了问题解的渐近性态并导出了几个有关的不等式，讨论了原问题解的存在唯一性和解的一致有效的渐近估计式．Abstract: A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered.Under suitable conditions,first,the outer solution of the original problem was obtained.Secondly,using the stretched variable,the composing expansion method and the expanding theory of power series the initial layer was constructed.Finally,using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied,and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.
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Key words:
- nonlinear /
- reaction diffusion /
- singular perturbation
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[1] de Jager E M,JIANG Fu-ru.The Theory of Singular Perturbation[M].Amsterdam:North-Holland Publishing Company,1996. [2] Hamouda M.Interior layer for second-order singular equations[J].Applicable Analysis,2002,81(2):837—866. doi: 10.1080/0003681021000004465 [3] Bell D C,Deng B.Singular perturbation of N-front traveling waves in the Fitzhugh-Nagumo equations[J].Nonlinear Analysis Real World Applications,2003,3(4):515—541. [4] do Nascimento A S.Stable transition layers in a semilinear diffusion equation with spatial inhomogeneties in N-dimensional domains[J].Journal of Differential Equations,2003,190(1):16—38. doi: 10.1016/S0022-0396(02)00147-X [5] MO Jia-qi.Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China,Ser A,1989,32(11):1306—1315. [6] MO Jia-qi,Shao S.The singularly perturbed boundary value problems for higher-order semilinear elliptic equations[J].Advances in Mathematics,2001,30(2):141—148. [7] MO Jia-qi,OUYANG Cheng.A class of nonlocal boundary value problems of nonlinear elliptic systems in unbounded domains[J].Acta Mathematica Scientia,2001,21(1):93—97. [8] MO Jia-qi.A class of nonlocal singularly perturbed problems for nonlinear hyperbolic differential equation[J].Acta Mathematicae Applicatae Sinica,2001,17(4):469—474. doi: 10.1007/BF02669699 [9] MO Jia-qi,ZHU Jiang,WANG Hui.Asymptotic behavior of the shock solution for a class of nonlinear equations[J].Progress in Natural Science,2003,13(9):768—770. doi: 10.1080/10020070312331344400 -
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