Analysis & PDE

  • Anal. PDE
  • Volume 4, Number 2 (2011), 341-367.

Well- and ill-posedness issues for energy supercritical waves

Slim Ibrahim, Mohamed Majdoub, and Nader Masmoudi

Full-text: Open access

Abstract

We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation. We also obtain some ill-posedness and weak ill-posedness results.

Article information

Source
Anal. PDE, Volume 4, Number 2 (2011), 341-367.

Dates
Received: 6 December 2009
Revised: 31 May 2010
Accepted: 29 June 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731128

Digital Object Identifier
doi:10.2140/apde.2011.4.341

Mathematical Reviews number (MathSciNet)
MR2859857

Zentralblatt MATH identifier
1267.35131

Subjects
Primary: 34C25: Periodic solutions 35L05: Wave equation 49K40: Sensitivity, stability, well-posedness [See also 90C31] 65F22: Ill-posedness, regularization

Keywords
nonlinear wave equation well-posedness ill-posedness finite speed of propagation oscillating second order ODE

Citation

Ibrahim, Slim; Majdoub, Mohamed; Masmoudi, Nader. Well- and ill-posedness issues for energy supercritical waves. Anal. PDE 4 (2011), no. 2, 341--367. doi:10.2140/apde.2011.4.341. https://projecteuclid.org/euclid.apde/1513731128


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