Local energy decay and Strichartz estimates for the wave equat ion with time periodic perturbations
Language
en
Article de revue
This item was published in
Progress in Nonlinear Diff. Equations and their Applications. 2006, vol. 69, p. 267-285
English Abstract
We examine the memorphic continuaiton of the cut-off resolvent Rχ(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 ...Read more >
We examine the memorphic continuaiton of the cut-off resolvent Rχ(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 Rχ(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 Rχ(z) for |z| > 1.Read less <
Origin
Hal imported