Spatially periodic contrast structures in singularly perturbed elliptic problems
The authors construct the asymptotics (as \(\varepsilon\to 0)\) for the solution of the following boundary value problem: \[ \varepsilon^2 \Delta u=f(u,x,y, \varepsilon), \quad (x,y) \in (0<x<1) \times (-\infty <y< \infty), \] \[ u(0,y, \varepsilon)= g_0(y),\;u(1,y, \varepsilon) =g_1 (y), \] where \(\varepsilon>0\) is a small parameter, and \(f\), \(g_0\) and \(g_1\) are sufficiently smooth functions that are \(L\)-periodic with respect to the variable \(y\).
scientific article; zbMATH DE number 1155320