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Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem 被引量:2

Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
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摘要 Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0(ε^2). Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0(ε^2).
作者 唐荣荣
出处 《Journal of Shanghai University(English Edition)》 CAS 2009年第1期12-15,共4页 上海大学学报(英文版)
基金 supported by the E-Institutes of Shanghai Municipal Education Commission (Grant No.E03004)
关键词 PERTURBATION reaction diffusion differential inequality asymptotic solution perturbation, reaction diffusion, differential inequality, asymptotic solution
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参考文献12

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