23. November 2020
Marcus Waurick (TU Hamburg und TU Graz)
Local and nonlocal homogenisation problems for Maxwell`s equations and beyond
Abstract:
In the talk, we shall describe a comprehensive class of time-dependent partial differential equations and address the continuous dependence of their solutions on the coefficients. For this, we introduce a new operator topology, which is strictly weaker than the strong operator and the norm topology and not comparable to the weak operator topology. We shall see that this topology is precisely the one needed to obtain continuity statements if one endows the solution operators in the weak operator topology. We show that bounded subsets of coefficients are relatively compact under the introduced topology, which leads the way to abstract $G$-compactness results in the context of homogenisation problems. Concerning particular applications, we shall devote our attention to the time-dependent Maxwell's equations.