Singular perturbation for the weakly nonlinear reaction diffusion equation with boundary perturbation |
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Authors: | Jia-qi Mo |
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Institution: | Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui Province, P. R. China;Department of Mathematics, Huzhou Teachers College, Huzhou 313000, Zhejiang Province, P, R. China;Division of Computational Science, E-Institutes of Shanghai Jiaotong University, Shanghai 200240,P.R. China |
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Abstract: | In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed. |
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Keywords: | nonlinear reaction diffusion singular perturbation boundary perturbation |
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