A class of nonlinear nonlocal singularly perturbed problems for reaction diffusion equations with boundary perturbation

莫嘉琪,; 王辉,; 林万涛,

doi:10.1007/bf03246277

Cited by 4 publications

(3 citation statements)

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“…Recently, many scholars such as O'Malley, Jr. [18] , Adams, King and Tew [1] , Bell and Deng [2] Butuzov, Nefedov and Schneider [3] , Hamouda [5] , Kelley [6] , have done a great deal of work. Using the method of differential inequalities and others Mo et al considered also a class of singularly perturbed nonlinear boundary value problems [7][8][9][10][11][12][13][14][15][16][17]. In this paper using a special and simple method, we study a class of singularly perturbed nonlinear reaction diffusion problem with boundary perturbation.…”

Section: Introductionmentioning

confidence: 98%

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

Jiaqi¹,

Mo²,

Wantao³

et al. 2006

Acta Mathematicae Applicatae Sinica, English Series

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Section: Introductionmentioning

confidence: 98%

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

Jiaqi¹,

Mo²,

Wantao³

et al. 2006

Acta Mathematicae Applicatae Sinica, English Series

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“…Asymptotic methods have been developed and refined, including the method of averaging boundary layer method, matched asymptotic expansion method and multiple scales method. Using the asymptotic method, Mo et al [6][7][8][9][10][11][12][13][14][15][16][17] considered also a class of singularly perturbed problems. In this paper, commencing the model of a class of laser pulse amplifier, by using the simple and valid homotopic mapping method [18] , we can rapidly solve for the approximate analytic solution with higher precision.…”

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confidence: 99%

Homotopic mapping solving method for gain fluency of a laser pulse amplifier

Jia-Qi

2009

Sci. China Ser. G-Phys. Mech. Astron.

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The model for gain fluency of a laser pulse amplifier is studied. Using the homotopic mapping method, firstly, the system of the original model is packed up standardization; secondly, introducing a homotopic mapping, taking the property of the mapping, inducing a contrived parameter, the solving of a nonlinear problem translates into the solving of a linear problem. Then the approximate expressions of the solution for the corresponding model are obtained. And the precision for the approximate solution is compared. It illuminates that the obtained approximate solution using the homotopic mapping method possesses higher approximate degree. At one time, the expansion of solution through the homotopic mapping method can be kept in the analytic operation. Thus it also enables us through differential and integral operations to obtain other physics behavior for the gain fluency of laser pulse amplifier. nonlinear, homotopic mapping, laser pulse amplifierThe laser pulse amplifier is a very attractive object of study in modern physics. It is an important project of manufacture for the famous China-II laser pulse amplifier [1][2][3][4] . In this investigation, we need to understand many physical behaviors, such as gain fluency, pulse undulance, density of photon, density of energy, gain of energy and so on. Lately, there has been more profound study for the without wasting laser pulse amplifier. But for the wasting laser pulse amplifier, there is lesser study [1,2] . There is difficulty that the exact solution of nonlinear differential equation can not obtained generally. Thus the numerical simulated or asymptotic method is used to obtain approximate solution. But we cannot use the analytic operation for the numerical simulated solution. It possesses determinate localization. On the other hand, we can use analytic operation by using the asymptotic method. And the homotopic map is a good asymptotic method.Recently, many scholars have investigated the approximate theory [3][4][5] . Asymptotic methods have been developed and refined, including the method of averaging boundary layer method, matched asymptotic expansion method and multiple scales method. Using the asymptotic method, Mo et al. [6][7][8][9][10][11][12][13][14][15][16][17] considered also a class of singularly perturbed problems. In this paper, commencing the model of a class of laser pulse amplifier, by using the simple and valid homotopic mapping method [18] , we can rapidly solve for the approximate analytic solution with higher precision. And then it provides further study of the physics behavior of laser pulse amplifier.

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“…For example, O'Malley, Jr. [7] , Butuzov, Nefedov and Schneider [3] , Kelley [6] , Hamouda [4] , Bell and Deng [2] and Adams, King and Tew [1] . Using the method of differential inequalities and others Mo et al considered a class of singularly perturbed nonlinear boundary value problems for the ordinary differential equations in [8,9], the reaction diffusion equations in [10,12], the boundary value problems of elliptic equations in [13,14], the initial boundary value problems of hyperbolic equations in [15], the shock layer solution of nonlinear equations for singularly perturbed problems in [16,17] and the problems of biomathematics in [18]. In this paper using a simple and special method, we study the asymptotic behavior of the solution for a singularly perturbed nonlinear reaction diffusion system, which has the initial and boundary layers.…”

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confidence: 99%