A method of joining asymptotic expansions for the equation $\varepsilon\Delta u-a(x,y)u_y=f(x,y)$ in a rectangle

In the closed rectangle ($0\leqslant x\leqslant l_1$, $0\leqslant y\leqslant l_2$) as $\varepsilon\to0$ an asymptotic expansion of the solution of the Dirichlet problem for the equation indicated in the title is constructed and proved. Near the corners $(0,0)$ and $(l_1,0)$ the method of joining two different asymptotic expansions is employed.
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