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Semigroup estimates and stability/instability results for the linearized three waves interaction equations

Abstract : We consider the three waves interaction system and its linearization (the "pump-wave approximation"). We give some estimates on the semigroup as well as stability or instability results for the linearized problem in suitable norms. We work in the whole space and with periodic boundary condition, and our analysis relies on energy estimates and not on the complete integrability of the system.
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Submitted on : Monday, April 8, 2013 - 3:38:39 PM
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David Chiron. Semigroup estimates and stability/instability results for the linearized three waves interaction equations. Revista Matematica Complutense, Universidad Complutense, 2012, 25, pp.285-333. ⟨10.1007/s13163-011-0070-y⟩. ⟨hal-00809134⟩

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