Highly oscillatory partial differential equations

Peter Markowich*, Christof Sparber

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Partial differential equations with highly oscillatory solutions occur in many areas of science like quantum mechanics and acoustics, with important spin-offs to semiconductors, nanotechnology and low-temperature physics. These equations pose a great challenge to mathematical and numerical analysis. Recently a new mathematical technique has been developed to treat highly oscillatory PDEs, namely Wigner transforms. They allow deep new insights into high-frequency asymptotics. The state-of-the-art is reported here, with emphasis on applications like quantum semiconductor devices and Bose-Einstein condensation.

Original languageEnglish (US)
Title of host publicationApplied Mathematics Entering the 21st Century
Subtitle of host publicationInvited Talks from the ICIAM 2003 Congress
EditorsJ.M. Hill, R. Moore
StatePublished - Jul 14 2004
EventApplied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress - Sydney, Australia
Duration: Jul 7 2004Jul 11 2004

Publication series

NameApplied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress

Other

OtherApplied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress
CountryAustralia
CitySydney
Period07/7/0407/11/04

ASJC Scopus subject areas

  • Engineering(all)

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