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Subjects
35-XX Partial differential equations
35Lxx Hyperbolic equations and systems
35L15 Initial value problems for second-order hyperbolic equations

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Finite difference approximations for partial differential equations with rapidly oscillating coefficients

M. Avellaneda, Th. Y. Hou, G. C. Papanicolaou (1991)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Free decay of solutions to wave equations on a curved background

Serge Alinhac (2005)

Bulletin de la Société Mathématique de France

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 $t^{- \frac{1}{2} - ε}$ along wave cones.

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