Applied Functional Analysis and Partial Differential Equations

In recent years there appeared a large number of papers, as well as chapters in more general monographs, devoted to evolution equations containing small (or large) parameters. This text gathers the existing literature and introduces new results concerning singularly perturbed evolution equations of the resonance type which are of interest in the applied sciences. This is particularly true in the case of kinetic theory which is chosen as a field of application for the asymptotic theory developed in the monograph Linear operators in Banach spaces; linear operators in Hilbert spaces; Sobolev spaces; semigroups of linear operators; weakly nonlinear evolution equations; semilinear parabolic equations