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Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 1996

Applications of the division theorem in $H^s$

Satyanad Kichenassamy

Résumé

We prove a version of the division theorem in Sobolev spaces with an estimate of the constant as $s$ tends to infinity. We then apply it to derive spatial decay estimates for time-periodic solutions of linear wave equations in one space dimension, and to prove that the space of decaying solutions is finite-dimensional. The main point is to show that some of the arguments used to analyze embedded eigenvalues of Schr\"odinger operators can be extended to cases where positivity arguments are not available. This has implications for nonlinear Klein-Gordon equations. A different approach, based on the proof of the stable manifold theorem, is also worked out, under slightly different assumptions.

Dates et versions

hal-00002656 , version 1 (20-08-2004)

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Satyanad Kichenassamy. Applications of the division theorem in $H^s$. Journal of Dynamics and Differential Equations, 1996, 8, pp.407-425. ⟨10.1007/BF02218761⟩. ⟨hal-00002656⟩

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