Highly oscillatory partial differential equations

Peter A. Markowich; Christof Sparber

Highly oscillatory partial differential equations

Peter A. Markowich^*, Christof Sparber

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 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 language	English (US)
Title of host publication	Applied Mathematics Entering the 21st Century
Subtitle of host publication	Invited Talks from the ICIAM 2003 Congress
Editors	J.M. Hill, R. Moore
Pages	288-312+xii
State	Published - 2004
Externally published	Yes
Event	Applied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress - Sydney, Australia Duration: Jul 7 2004 → Jul 11 2004

Publication series

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

Other

Other	Applied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress
Country/Territory	Australia
City	Sydney
Period	07/7/04 → 07/11/04

ASJC Scopus subject areas

General Engineering

Cite this

@inproceedings{05767def6cef43b187aa249b3bac54a8,

title = "Highly oscillatory partial differential equations",

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.",

author = "Markowich, {Peter A.} and Christof Sparber",

year = "2004",

language = "English (US)",

isbn = "0898715598",

series = "Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress",

pages = "288--312+xii",

editor = "J.M. Hill and R. Moore",

booktitle = "Applied Mathematics Entering the 21st Century",

note = "Applied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress ; Conference date: 07-07-2004 Through 11-07-2004",

}

Markowich, PA & Sparber, C 2004, Highly oscillatory partial differential equations. in JM Hill & R Moore (eds), Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress. Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress, pp. 288-312+xii, Applied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress, Sydney, Australia, 07/7/04.

Highly oscillatory partial differential equations. / Markowich, Peter A.; Sparber, Christof.
Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress. ed. / J.M. Hill; R. Moore. 2004. p. 288-312+xii (Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Markowich, Peter A.

AU - Sparber, Christof

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:3042710051

SN - 0898715598

SN - 9780898715590

T3 - Applied Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003 Congress

SP - 288-312+xii

BT - Applied Mathematics Entering the 21st Century

A2 - Hill, J.M.

A2 - Moore, R.

T2 - Applied Mathematics Entering the 21st Century: Invited Talks from theICIAM 2003 Congress

Y2 - 7 July 2004 through 11 July 2004

ER -

Highly oscillatory partial differential equations

Abstract

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ASJC Scopus subject areas

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