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Russian Mathematical Surveys, 2010, Volume 65, Issue 1, Pages 95–142
DOI: https://doi.org/10.1070/RM2010v065n01ABEH004662 (Mi rm9340) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Dispersive estimates for the Schrödinger and Klein–Gordon equations

E. A. Kopylova

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
English version PDF (749 kB) Citations (13)
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DOI: https://doi.org/10.1070/RM2010v065n01ABEH004662
Abstract: This is a survey of results on the long-time asymptotic behaviour of solutions of the Schrödinger and Klein–Gordon equations in weighted energy norms. Results obtained from 1975 to 2001 in the spectral scattering theory of Agmon, Jensen–Kato, Jensen–Nenciu, and Murata are described for the Schrödinger equation, along with the author's recent results [1]–[3] obtained jointly with A. I. Komech for the Klein–Gordon equation. The methods used develop the spectral approach as applied to relativistic equations.
Bibliography: 40 titles.
Keywords: Schrödinger equation, Klein–Gordon equation, Cauchy problem, long-time asymptotic behaviour, weighted spaces.
Received: 21.12.2009
Russian version:
Uspekhi Matematicheskikh Nauk, 2010, Volume 65, Issue 1(391), Pages 97–144
DOI: https://doi.org/10.4213/rm9340
Bibliographic databases:
Document Type: Article
UDC: 517.955+517.958
MSC: 35B40, 35P05
Language: English
Original paper language: Russian
Citation: E. A. Kopylova, “Dispersive estimates for the Schrödinger and Klein–Gordon equations”, Uspekhi Mat. Nauk, 65:1(391) (2010), 97–144; Russian Math. Surveys, 65:1 (2010), 95–142
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
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