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Well- and ill-posedness
issues for energy supercritical waves
Slim Ibrahim, Mohamed Majdoub and Nader Masmoudi |
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Vol. 4 (2011), No. 2, 341–367
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Abstract |
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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. |
Keywords
nonlinear wave equation, well-posedness, ill-posedness,
finite speed of propagation, oscillating second order ODE
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Mathematical Subject Classification 2000
Primary: 34C25, 35L05, 49K40, 65F22
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Milestones
Received: 6 December 2009
Revised: 31 May 2010
Accepted: 29 June 2010
Published: 18 November 2011
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Authors |
| Slim Ibrahim | |
| Department of Mathematics and
Statistics University of Victoria PO Box 3060 STN CSC Victoria V8P 5C3 Canada |
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| Mohamed Majdoub | |
| Department of Mathematics University of Tunis El Manar Campus Universitaire 2092 Tunis Tunisia |
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| Nader Masmoudi | |
| Courant Institute for Mathematical
Sciences New York University New York, NY 10012-1185 United States |
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