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Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem. (English) Zbl 1200.35046
Summary: We consider a singularly perturbed elliptic convection-diffusion problem on the unit square. A new asymptotic expansion of its solution is constructed, giving precise conditions under which the solution can be decomposed in a particularly opportune way into a sum of smooth and layer functions.

MSC:
35C20 Asymptotic expansions of solutions to PDEs
35B25 Singular perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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