Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation

Di Pomponio, Stefania. "Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation." Serdica Mathematical Journal 26.2 (2000): 127-144. <http://eudml.org/doc/11484>.

@article{DiPomponio2000,
abstract = {The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodi nella Teoria delle Equazioni Iperboliche”.We treat the oscillatory problem for semilinear wave equation. The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x). By using suitable variants of Strichartz estimate we extend the results from [6] on a priori estimates of the approximations of geometric optics.The main improvement is the fact that we can obtain a priori estimates for the case σ = 1, while in [6] we could treat only the case σ > n/2 − 1.},
author = {Di Pomponio, Stefania},
journal = {Serdica Mathematical Journal},
keywords = {Semilinear Wave Equation; Strichartz Estimate; oscillatory initial data; periodic boundary conditions},
language = {eng},
number = {2},
pages = {127-144},
publisher = {Institute of Mathematics and Informatics},
title = {Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation},
url = {http://eudml.org/doc/11484},
volume = {26},
year = {2000},
}

TY - JOUR
AU - Di Pomponio, Stefania
TI - Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation
JO - Serdica Mathematical Journal
PY - 2000
PB - Institute of Mathematics and Informatics
VL - 26
IS - 2
SP - 127
EP - 144
AB - The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodi nella Teoria delle Equazioni Iperboliche”.We treat the oscillatory problem for semilinear wave equation. The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x). By using suitable variants of Strichartz estimate we extend the results from [6] on a priori estimates of the approximations of geometric optics.The main improvement is the fact that we can obtain a priori estimates for the case σ = 1, while in [6] we could treat only the case σ > n/2 − 1.
LA - eng
KW - Semilinear Wave Equation; Strichartz Estimate; oscillatory initial data; periodic boundary conditions
UR - http://eudml.org/doc/11484
ER -