Spectral theory and nonlinear partial differential equations: A survey

Wilhelm Schlag

doi:10.3934/dcds.2006.15.703

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2006, Volume 15, Issue 3: 703-723. Doi: 10.3934/dcds.2006.15.703

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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

Received: October 2005

Revised: January 2006

Published: September 2006

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Abstract

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:

Focusing NLS and NLW,
criticality,
orbital and asymptotic stability of stationary waves,
spectral theory.

Mathematics Subject Classification: Primary: 35B35, 35B40; Secondary: 35Q51, 35Q55.

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