Homogenization of some linear and semilinear Schrödinger equations with real potential (Q5946702)

This paper considers initial-boundary value problems for linear and semilinear Schrödinger equations with coefficients, depending on a small parameter \(\varepsilon >0\), and a real potential. The initial data are assumed to be in \(H^1_0(\Omega)\), where \(\Omega\) is a bounded open domain of \(\mathbb R^N\), \(N\geqslant 3\), and they also depend on the same parameter \(\varepsilon\). A result on convergence (as \(\varepsilon \to 0\)) of solutions to a solution of the corresponding homogenized problem is given.