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.

We investigate for which metric g (close to the standard metric g 0 ) 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 g-g 0 ; in particular, g-g 0 decays like t -1 2-ε along wave cones.

Nous étudions pour quelles métriques g (proches de la métrique standard g 0 ) les solutions du d’Alembertien pour g 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 g-g 0  ; en particulier, g-g 0 décroît comme t -1 2-ε le long des cônes d’onde.

DOI: 10.24033/bsmf.2493
Classification: 35L40
Keywords: energy inequality, wave equation, decay of solutions
Mot clés : inégalité d'énergie, équation des ondes, décroissance des solutions
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     title = {Free decay of solutions to wave equations on a curved background},
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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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