Singularly perturbed evolution equations with applications to kinetic theory

This text provides a presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a presentation of necessary background materials and by the working out of many examples 1. Introduction -- 2. Mathematical preliminaries -- 3. Semigroup theory -- 4. Development of asymptotic methods for singularly perturbed evolution equations -- 5. Some singular-singularly perturbed evolution equations and kinetic equation -- 6. Hilbert space theory for equations of kinetic type -- 7. Applications to kinetic equations with bounded collision operators -- 8. Applications to equations of Fokker-Planck type -- 9. Applications to spatially inhomogeneous linear Boltzmann equation -- 10. Application to kinetic equation with external field -- 11. Miscellaneous results