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The role of the error function in a singularly perturbed convection-diffusion problem in a rectangle with corner singularities. (English) Zbl 1174.35032

The authors deal with an two-dimensional linear elliptic convection-diffusion problems: find a function uC(Ω ¯)D 2 (Ω) such that

-εΔu+v·u=0,xΩ 2 ,
u| Ω =f(x ˜),x ˜Ω,

where ε is a small positive parameter, V is the convection vector, x ˜ is a variable which lives in Ω, and D 2 (Ω) is the set of functions with partial derivatives up to order two defined in all points of Ω. The authors derive asymptotic expansion of the solution for ε0. Moreover, they derive also asymptotic approximations near the points of discontinuity of the boundary condition.

MSC:
35J25Second order elliptic equations, boundary value problems
35B25Singular perturbations (PDE)
35C20Asymptotic expansions of solutions of PDE