Singularly perturbed differential equations with discontinuous coefficients and concentrated factors

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In this paper singularly perturbed one-dimensional reaction–diffusion equations with discontinuous coefficients and concentrated factors are examined. A new formulation which allows us to reduce the solving of general interface problems to the corresponding ones with only discontinuous coefficients is proposed. Then, a decomposition of the solution of the problem with only discontinuous coefficients into regular and singular parts (Shishkin decomposition) is derived. Asymptotic expansion up to fourth-order for the solution in the interfaces is also constructed.