Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. (English) Zbl 0951.35102
Summary: Consider a propagator defined on a Banach space whose norm satisfies an appropriate exponential bound. To this operator is added a bounded operator which is relatively smoothing in the sense of Vidav. The location of the essential spectrum of the perturbed propagator is then estimated. An application to kinetic theory is given for a system of particles that interact both through collisions and through their charges.
MSC:
35P05 | General topics in linear spectral theory for PDEs |
35Q99 | Partial differential equations of mathematical physics and other areas of application |
47D06 | One-parameter semigroups and linear evolution equations |
47N20 | Applications of operator theory to differential and integral equations |
76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
82C40 | Kinetic theory of gases in time-dependent statistical mechanics |