TY  - BOOK
AU  - Ringstrom,Hans
TI  - Linear systems of wave equations on cosmological backgrounds with convergent asymptotics
T2  - Asterisque
SN  - 9782856299265
U1  - 530.12 23
PY  - 2020///
CY  - Paris
PB  - Societe Mathematique de France, 
KW  - Hyperbolic Equations on Manifolds
KW  - Wave Equations
KW  - Asymptotic Behavior
KW  - Energy estimates
KW  - Lorentz Manifolds
KW  - General Relativity
KW  - Cosmology
N1  - Includes index and bibliographical references; Pari I. Introductory material results -- 1. Equations and questions -- 2. On the notion of balance -- 3. A geometric perspective -- 4. Silent equations -- 5. Transparent equations -- 6. Equations with a dominant noisy spatial direction -- 7. Energy estimates in the asymptotically diagonal setting -- 8. Improved asymptotic estimates in the silent setting -- Part II. Rough analysis in the silent and in the transparent settings -- 9. ODE's with exponentially decaying error terms -- 10. Asymptotics for weakly silent balanced and convergent equations -- 11. ODE analysis in the transparent setting -- 12. Asymptotics for weakly transparent balanced and convergent equations -- Part III. Averaging over oscillations -- 13. Introduction and technical preliminaries -- 14. One period of the oscillations terminology and preliminary estimates -- 15. One period of the oscillations reformulation and detailed estimates --  Part IV. Unbalanced equations -- 16. Unbalanced equations -- Part V. Equations with a dominant noisy spatial direction -- 17. Terminology and basic estimates -- 18. Asymptotics for one mode and late times -- 19. Asymptotics for all future times -- Part VI. Non-degenerate diagonally dominated convergent and balanced equations -- 20. Equations with diagonally dominated convergent and balanced coefficients -- 21. Non-degenerate diagonally dominated convergent and balanced equations -- 22. Estimating the Sobolev norms of solutions -- 23. The silent setting -- Part Vii Appendices -- 24. Spectral aspects of differential operators and marrices -- 25. Geometric preliminaries -- 26. Relating the analytic and geometric conditions -- Index -- Bibliography
ER  -