Non-existence of a gap in the eigenvalue spectrum of the linearized collision operator of Peierls' phonon-Boltzmann equation
✍ Scribed by Josef Jäckle
- Book ID
- 112747394
- Publisher
- Springer
- Year
- 1970
- Tongue
- English
- Weight
- 247 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1434-6036
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📜 SIMILAR VOLUMES
The phonon spectrum of a one-dimensional lattice with masses varying incommensurately with the underlying lattice is studied by a discrete version of a multiple-scale perturbation theory. From the resonances in the higher order correction terms we determine the location of the gaps in the spectrum.
A contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non-linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the