Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

Kian, Yavar. "Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates." Serdica Mathematical Journal 35.4 (2010): 329-370. <http://eudml.org/doc/281428>.

@article{Kian2010,
abstract = {2000 Mathematics Subject Classification: 35B40, 35L15.We obtain local energy decay as well as global Strichartz estimates for the solutions u of the wave equation ∂t2 u-divx(a(t,x)∇xu) = 0, t ∈ R, x ∈ Rn, with time-periodic non-trapping metric a(t,x) equal to 1 outside a compact set with respect to x. We suppose that the cut-off resolvent Rχ(θ) = χ(U(T, 0)− e−iθ)−1χ, where U(T, 0) is the monodromy operator and T the period of a(t,x), admits an holomorphic continuation to \{θ ∈ C : Im(θ) ≥ 0\}, for n ≥ 3, odd, and to \{θ ∈ C : Im(θ) ≥ 0, θ ≠ 2kπ − iμ, k ∈ Z, μ ≥ 0\} for n ≥ 4, even, and for n ≥ 4 even Rχ(θ) is bounded in a neighborhood of θ = 0.},
author = {Kian, Yavar},
journal = {Serdica Mathematical Journal},
keywords = {Time-Dependent Perturbation; Non-Trapping Metric; Local Energy Decay; Strichartz Estimates; time-dependent perturbation; non-trapping metric; local energy decay; Strichartz estimates},
language = {eng},
number = {4},
pages = {329-370},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates},
url = {http://eudml.org/doc/281428},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Kian, Yavar
TI - Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates
JO - Serdica Mathematical Journal
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 4
SP - 329
EP - 370
AB - 2000 Mathematics Subject Classification: 35B40, 35L15.We obtain local energy decay as well as global Strichartz estimates for the solutions u of the wave equation ∂t2 u-divx(a(t,x)∇xu) = 0, t ∈ R, x ∈ Rn, with time-periodic non-trapping metric a(t,x) equal to 1 outside a compact set with respect to x. We suppose that the cut-off resolvent Rχ(θ) = χ(U(T, 0)− e−iθ)−1χ, where U(T, 0) is the monodromy operator and T the period of a(t,x), admits an holomorphic continuation to {θ ∈ C : Im(θ) ≥ 0}, for n ≥ 3, odd, and to {θ ∈ C : Im(θ) ≥ 0, θ ≠ 2kπ − iμ, k ∈ Z, μ ≥ 0} for n ≥ 4, even, and for n ≥ 4 even Rχ(θ) is bounded in a neighborhood of θ = 0.
LA - eng
KW - Time-Dependent Perturbation; Non-Trapping Metric; Local Energy Decay; Strichartz Estimates; time-dependent perturbation; non-trapping metric; local energy decay; Strichartz estimates
UR - http://eudml.org/doc/281428
ER -