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August  2006, 15(3): 703-723. doi: 10.3934/dcds.2006.15.703

Spectral theory and nonlinear partial differential equations: A survey

Wilhelm Schlag 1,

1. 

The University of Chicago, Department of Mathematics, 5734 South University Ave., Chicago, IL 60637, United States

Received  October 2005 Revised  January 2006 Published  April 2006

This paper reviews some of the recent work of the author on stable manifolds for unstable evolution equations. In particular, we discuss such a result, jointly with Joachim Krieger, for the critical focusing nonlinear wave equation in three dimensions.
Keywords: orbital and asymptotic stability of stationary waves, Focusing NLS and NLW, spectral theory., criticality.
Mathematics Subject Classification: Primary: 35B35, 35B40; Secondary: 35Q51, 35Q5.
Citation: Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703
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