Long-Time Dispersive Estimates for Perturbations of a Kink Solution of One-Dimensional Cubic Wave Equations

Jean-Marc Delort
Université Sorbonne Paris-Nord, France
Nader Masmoudi
New York University Abu Dhabi, United Arab Emirates; Courant Institute of Mathematical Sciences, USA

This book is published open access.

	AbstractDownload p. v
	ContentsDownload pp. vii–ix
1	IntroductionDownload pp. 1–30
2	The kink problemDownload pp. 31–51
3	First quadratic normal formDownload pp. 53–57
4	Construction of approximate solutionsDownload pp. 59–80
5	Reduced form of dispersive equationDownload pp. 81–102
6	Normal formsDownload pp. 103–115
7	Bootstrap: $L^{2}$ -estimatesDownload pp. 117–138
8	$L^{\infty}$ estimates and end of bootstrapDownload pp. 139–154
A	Scattering for time independent potentialDownload pp. 155–163
B	(Semiclassical) pseudo-differential operatorsDownload pp. 165–176
C	Bounds for forced linear Klein–Gordon equationsDownload pp. 177–201
D	Action of multilinear operators on Sobolev and Hölder spacesDownload pp. 203–227
E	Wave operators for time dependent potentialsDownload pp. 229–252
F	Division lemmas and normal formsDownload pp. 253–267
G	Verification of Fermi’s golden ruleDownload pp. 269–271
	ReferencesDownload pp. 273–277
	List of notationDownload pp. 279–280