by J R Mika (University of Natal, South Africa) & J Banasiak (University of Natal, South Africa)

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. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.

• Introduction
• Mathematical Preliminaries
• Semigroup Theory
• Development of Asymptotic Methods for Singularly Perturbed Evolution Equations
• Some Singular-Singularly Perturbed Evolution Equations and Kinetic Equation
• Hilbert Space Theory for Equations of Kinetic Type
• Applications to Kinetic Equations with Bounded Collision Operators
• Applications to Equations of Fokker-Planck Type
• Applications to Spatially Inhomogeneous Linear Boltzmann Equation
• Application to Kinetic Equation with External Field
• Miscellaneous Results