Damped Wave Equations on Compact Hyperbolic Surfaces

Damped Wave Equations on Compact Hyperbolic Surfaces

We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov and Jin (Acta Math 220:297–339, DyJi18) and in particular, uses the fra...

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Veröffentlicht in:Communications in mathematical physics 2020-02, Vol.373 (3), p.771-794
1. Verfasser: Jin, Long
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Damping
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Wave equations
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Zusammenfassung:We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov and Jin (Acta Math 220:297–339, DyJi18) and in particular, uses the fractal uncertainty principle proved in Bourgain and Dyatlov (Ann Math (2) 187:825–867, BoDy18).
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03650-x