Abstract
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
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Supported by the National Natural Science Foundation of China (90111011 and 10471039), the National Key Project for Basics Research (2003CB415101-03 and 2004CB418304), the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221) and the Natural Science Foundation of Zhejiang (Y604127).
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Yao, J., Mo, J. The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations with a boundary perturbation. Anal. Theory Appl. 21, 242–248 (2005). https://doi.org/10.1007/BF02836954
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DOI: https://doi.org/10.1007/BF02836954