On operator norm convergence in time‐dependent homogenisation problems
Marcus Waurick · PAMM · 2018
Abstract Using the d‐dimensional wave equation as a prime example, we shall show that an elementary functional analytic theorem for compact operators leads to operator norm convergence of the solution operators of the homogenisation for the wave equation considered as operators in space‐time. The results imply convergence of the amplitude functions locally in L2 with respect to the temporal and globally in L2 with respect to the spatial variables.