Abstract
In this paper, we address the existence and asymptotic analysis of higher-dimensional contrast structure of singularly perturbed Dirichlet problem. Based on the existence, an asymptotical analysis of a steplike contrast structure (i.e., an internal transition layer solution) is studied by the boundary function method via a proposed smooth connection. In the framework of this paper, we propose a first integral condition, under which the existence of a heteroclinic orbit connecting two equilibrium points is ensured in a higher-dimensional fast phase space. Then, the step-like contrast structure is constructed, and the internal transition time is determined. Meanwhile, the uniformly valid asymptotical expansion of such an available step-like contrast structure is obtained. Finally, an example is presented to illustrate the result.
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Ni, M., Wang, Z. On higher-dimensional contrast structure of singularly perturbed Dirichlet problem. Sci. China Math. 55, 495–507 (2012). https://doi.org/10.1007/s11425-012-4375-1
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DOI: https://doi.org/10.1007/s11425-012-4375-1