July  1999, 5(3): 457-472. doi: 10.3934/dcds.1999.5.457

Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system

1. 

Department of Mathematics, Indiana University, Bloomington, IN 47405{5701, United States

2. 

Department of Mathematics and LCDS, Brown University, Providence, RI 02912, United States

Received  February 1999 Revised  May 1999 Published  May 1999

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.
Citation: Robert T. Glassey, Walter A. Strauss. Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 457-472. doi: 10.3934/dcds.1999.5.457
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