We investigate for which metric (close to the standard metric ) the solutions of the corresponding d’Alembertian behave like free solutions of the standard wave equation. We give rather weak (i.e., non integrable) decay conditions on ; in particular, decays like along wave cones.
Nous étudions pour quelles métriques (proches de la métrique standard ) les solutions du d’Alembertien pour se comportent comme des solutions libres de l’équation des ondes standard. Nous proposons des conditions de décroissance assez faibles (i.e., non intégrables) sur ; en particulier, décroît comme le long des cônes d’onde.
Keywords: energy inequality, wave equation, decay of solutions
Mot clés : inégalité d'énergie, équation des ondes, décroissance des solutions
@article{BSMF_2005__133_3_419_0, author = {Alinhac, Serge}, title = {Free decay of solutions to wave equations on a curved background}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {419--458}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {133}, number = {3}, year = {2005}, doi = {10.24033/bsmf.2493}, mrnumber = {2169825}, zbl = {1096.35013}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/bsmf.2493/} }
TY - JOUR AU - Alinhac, Serge TI - Free decay of solutions to wave equations on a curved background JO - Bulletin de la Société Mathématique de France PY - 2005 SP - 419 EP - 458 VL - 133 IS - 3 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/bsmf.2493/ DO - 10.24033/bsmf.2493 LA - en ID - BSMF_2005__133_3_419_0 ER -
%0 Journal Article %A Alinhac, Serge %T Free decay of solutions to wave equations on a curved background %J Bulletin de la Société Mathématique de France %D 2005 %P 419-458 %V 133 %N 3 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/bsmf.2493/ %R 10.24033/bsmf.2493 %G en %F BSMF_2005__133_3_419_0
Alinhac, Serge. Free decay of solutions to wave equations on a curved background. Bulletin de la Société Mathématique de France, Volume 133 (2005) no. 3, pp. 419-458. doi : 10.24033/bsmf.2493. http://archive.numdam.org/articles/10.24033/bsmf.2493/
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