# Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation

Serdica Mathematical Journal (2000)

- Volume: 26, Issue: 2, page 127-144
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topDi 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.