Singularly Perturbed Solution for Semilinear Reaction Diffusion Equations With Two Parameters
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摘要: 讨论了一类具有双参数的半线性反应扩散方程奇摄动初始边值问题.利用微分不等式理论,研究了初始边值问题解的渐近性态.Abstract: A class of singularly perturbed initial boundary value problem for semilinear reaction diffusion equations with two parameters was considered. Under suitable conditions, using theory of differential inequalities, the existence and asymptotic behavior of solution for initial boundary value problem were studied.
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Key words:
- nonlinear /
- two parameters /
- singular perturbation /
- reaction diffusion /
- initial layer /
- boundary layer
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[1] de Jager E M,JIANG Fu-ru.The Theory of Singular Perturbation[M].Amsterdam:North-Holland Publishing Co,1996. [2] NI Wei-ming,WEI Jun-cheng.On positive solution concentrating on spheres for the Gierer-Meinhardt system[J].J Differential Equations,2006,221(1):158-189. doi: 10.1016/j.jde.2005.03.004 [3] Zhang F.Coexistence of a pulse and multiple spikes and transition layers in the standing waves of a reaction-diffusion system[J].J Differential Equations,2004,205(1):77-155. doi: 10.1016/j.jde.2004.06.017 [4] Khasminskii R Z,Yin G.Limit behavior of two-time-scale diffusion revisited[J].J Differential Equations,2005,212(1):85-113. doi: 10.1016/j.jde.2004.08.013 [5] Marques I.Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann condition[J].Nonlinear Anal,2005,61(1):21-40. doi: 10.1016/j.na.2004.11.006 [6] Bobkova A S.The behavior of solutions of multidimensional singularly perturbed system with one fast variable[J].J Differential Equations,2005,41(1):23-32. [7] MO Jia-qi.A singularly perturbed nonlinear boundary value problem[J].J Math Anal Appl,1993,178(1):289-293. doi: 10.1006/jmaa.1993.1307 [8] MO Jia-qi.Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China,Ser A,1989,32(11):1306-1315. [9] MO Jia-qi,LIN Wan-tao.A nonlinear singular perturbed problem for reaction diffusion equations with boundary perturbation[J].Acta Math Appl Sinica,2005,21(1):101-104. doi: 10.1007/s10255-005-0220-4 [10] MO Jia-qi,LIN Wan-tao.Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J].J Sys Sci & Complexity,2008,20(1):119-128. [11] MO Jia-qi,Shao S.The singularly perturbed boundary value problems for higher-order semilinear elliptic equations[J].Advances in Math,2001,30(2):141-148. [12] MO Jia-qi,WANG Hui.Nonlinear singularly perturbed approximate solution for generalized Lotke-Volterra ecological model[J].Acta Ecologica Sinica,2007,27(10):4366-4370. [13] MO Jia-qi,ZHU Jiang,WANG Hui.Asymptotic behavior of the shock solution for a class of nonlinear equations[J].Prog Nat Sci,2003,13(9):768-770. doi: 10.1080/10020070312331344400 [14] MO Jia-qi,HAN Xiang-lin.Asymptotic shock solution for a nonlinear equation[J].Acta Math Sci,2004,24(2):164-167. [15] MO Jia-qi,LIN Wan-tao,WANG Hui.Variational iteration solving method of a sea-air oscillator model for the ENSO[J].Prog Nat Sci,2007,17(2):230-232. doi: 10.1080/10020070612331343252 [16] MO Jia-qi,LIN Wan-tao,WANG Hui.Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific[J].Chin Phys,2007,16(4):951-964. doi: 10.1088/1009-1963/16/4/016 [17] MO Ji-aqi,LIN Wan-tao.Asymptotic solution for a class of sea-air oscillator model for El-Nino-southern oscillation[J].Chin Phys,2008,17(2):370-372. doi: 10.1088/1674-1056/17/2/002 [18] MO Jia-qi,LIN Wan-tao,WANG Hui.Singularly perturbed solution of coupled model in atmosphere-ocean for global climate[J].Chin Geographical Sci,2008,18(2):193-195. doi: 10.1007/s11769-008-0193-3
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