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.