Well- and ill-posedness issues for energy supercritical waves

Slim Ibrahim; Mohamed Majdoub; Nader Masmoudi

doi:10.2140/apde.2011.4.341

Well- and ill-posedness issues for energy supercritical waves

Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	341-367
Number of pages	27
Journal	Analysis and PDE
Volume	4
Issue number	2
DOIs	https://doi.org/10.2140/apde.2011.4.341
State	Published - 2011

Keywords

Finite speed of propagation
Ill-posedness
Nonlinear wave equation
Oscillating second order ODE
Well-posedness

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2011.4.341

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AB - 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.

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KW - Oscillating second order ODE

KW - Well-posedness

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Well- and ill-posedness issues for energy supercritical waves

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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