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Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations

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Phase Space Analysis of Partial Differential Equations

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 69))

Abstract

We examine the memorphic continuation of the cut-off resolvent R χ(z) = χ(U(T, 0) ∊ z)−1χ, χ(x) ∊ C ∞0 (ℝn), where U(t, s) is the propagator related to the wave equation with non-trapping time-periodic perturbations (potential V (t, x) or a periodically moving obstacle) and T > 0 is the period. Assuming that R χ(z) has no poles z with |z| ≥ 1, we establish a local energy decay and we obtain global Strichartz estimates. We discuss the case of trapping moving obstacles and we present some results and conjectures concerning the behavior of R χ(z) for |z| > 1.

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Authors and Affiliations

  1. Département de Mathématiques Appliquées, Université Bordeaux 1, Talence, France

    Vesselin Petkov

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  1. Vesselin Petkov
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, I-40126, Bologna, Italy

    Antonio Bove

  2. Dipartimento di Matematica, Università di Pisa, I-56127, Pisa, Italy

    Ferruccio Colombini

  3. Dipartimento di Scienze Matematiche, Università di Trieste, I-34127, Trieste, Italy

    Daniele Del Santo

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© 2006 Birkhäuser Boston

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Petkov, V. (2006). Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations. In: Bove, A., Colombini, F., Del Santo, D. (eds) Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 69. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4521-2_14

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