Asymptotic analysis of the diffusion-absorption equation with fast and strongly oscillating absorbtion coefficient in the two-dimensional case (Q2447022)

The author considers the Helmholtz equation with fast oscillating absorbtion coefficient \[ -{\partial^2u\over\partial x_1}-{\partial^2u\over\partial x_2}+q({x_1\over\epsilon})u=f(x_1,x_2) \] on a square with zero Dirichlet condition on the left and right sides and zero Neumann condition on the top and bottom, where \(\epsilon\) is small. An asymptotic solution is constructed.