The aim of this Note is to present dispersive estimates for strictly hyperbolic equations with time dependent coefficients that have integrable derivatives. We will relate the time decay rate of norms of solutions to certain geometric indices associated to the characteristics of the limiting equation. Results will be applied to the global solvability of Kirchhoff type equations with small data, and to the dispersive estimates for their solutions.
Dans cette Note, nous établissons des estimations dispersives des solutions d'équations strictement hyperboliques à coefficients dépendant du temps et à dérivées intégrables. Nous estimons le taux de décroissance en temps des normes des solutions en fonction d'indices géométriques associés aux caractéristiques de l'équation limite. Les résultats sont appliqués à la résolvabilité globale des équations de type Kirchhoff à données petites et à des estimations dispersives des solutions.
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@article{CRMATH_2009__347_15-16_915_0, author = {Matsuyama, Tokio and Ruzhansky, Michael}, title = {Time decay for hyperbolic equations with homogeneous symbols}, journal = {Comptes Rendus. Math\'ematique}, pages = {915--919}, publisher = {Elsevier}, volume = {347}, number = {15-16}, year = {2009}, doi = {10.1016/j.crma.2009.06.010}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.06.010/} }
TY - JOUR AU - Matsuyama, Tokio AU - Ruzhansky, Michael TI - Time decay for hyperbolic equations with homogeneous symbols JO - Comptes Rendus. Mathématique PY - 2009 SP - 915 EP - 919 VL - 347 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.06.010/ DO - 10.1016/j.crma.2009.06.010 LA - en ID - CRMATH_2009__347_15-16_915_0 ER -
%0 Journal Article %A Matsuyama, Tokio %A Ruzhansky, Michael %T Time decay for hyperbolic equations with homogeneous symbols %J Comptes Rendus. Mathématique %D 2009 %P 915-919 %V 347 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.06.010/ %R 10.1016/j.crma.2009.06.010 %G en %F CRMATH_2009__347_15-16_915_0
Matsuyama, Tokio; Ruzhansky, Michael. Time decay for hyperbolic equations with homogeneous symbols. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 915-919. doi : 10.1016/j.crma.2009.06.010. http://www.numdam.org/articles/10.1016/j.crma.2009.06.010/
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