Spectral Properties and Stability of Self-Similar Wave Maps
| Preis: | 69.90 EUR* (inkl. MWST zzgl. Versand - Preis kann jetzt höher sein!) |
| Versand: | 0.00 EUR Versandkostenfrei innerhalb von Deutschland |
| Partner: | buecher.de |
| Hersteller: | Südwestdeutscher Verlag Für Hochschulschriften (Donninger, Roland) |
| Stand: | 2015-08-04 03:50:33 |
Produktbeschreibung
In this thesis the Cauchy problem and in particular the question of singularity formation for co-rotational wave maps from Minkowski space to the three-sphere is studied. Numerics indicate that self-similar solutions play a crucial role in dynamical time evolution. In particular, it is conjectured that a certain solution f defines a universal blow up pattern in the sense that the future development of a large set of generic blow up initial data approaches f. Thus, singularity formation is closely related to stability properties of self-similar solutions. In this work, the problem of linear stability is studied by functional analytic methods. In particular, a complete spectral analysis of the perturbation operators is given and well-posedness of the linearized Cauchy problem is proved by means of semigroup theory and, alternatively, the functional calculus for self-adjoint operators. These results lead to growth estimates which provide information on the stability of self-similar wave maps. The thesis is intended to be self-contained, i.e. all the mathematical requirements are carefully introduced, including proofs for many results which could be found elsewhere.
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