Analyses of Approximate Models

In this chapter, we specifically study the approximate models that we derived from Maxwell’s equations. We refer to Chap. 1 for the models, and we rely on the mathematical tools introduced in Chaps. 2, 3 and 4. Unless otherwise specified, we consider complex-valued function spaces. Constants that are independent of the data, but that may depend on the domain or on the parameters defining the model, are generically denoted by C, C0, C1, etc. We provide incremental proofs for the well-posedness of the static, quasi-static and Darwin models, in the sense that solving the quasi-static models relies on the solution of static problems, whereas solving the Darwin models relies on the solution of static and quasi-static problems.