Linking hyperbolic and parabolic p.d.e.’s

Heiko J. Zwart; Yann Le Gorrec; Bernhard Maschke

doi:10.1109/CDC.2011.6160422

Linking hyperbolic and parabolic p.d.e.’s

Heiko J. Zwart
, Yann Le Gorrec
, Bernhard Maschke

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

5 Citations (Scopus)

10 Downloads (Pure)

Abstract

In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.’s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain existence and uniqueness of solutions for the uniform elliptic p.d.e.’s and for the Schrodinger equation.

Original language	English
Title of host publication	Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	4921-4924
Number of pages	4
ISBN (Electronic)	978-1-61284-801-3, 978-1-61284-799-3
ISBN (Print)	978-1-61284-800-6, 9978-1-4673-0457-3 (CD)
DOIs	https://doi.org/10.1109/CDC.2011.6160422
Publication status	Published - Dec 2011
Event	50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - USA, United States Duration: 12 Dec 2011 → 15 Dec 2011 Conference number: 50

Publication series

Name	IEEE Conference on Decision and Control and European Control Conference
Publisher	IEEE Control Systems Society
Volume	2011
ISSN (Print)	0191-2216
ISSN (Electronic)	0743-1546

Conference

Conference	50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Abbreviated title	CDC-ECC
Country/Territory	United States
City	USA
Period	12/12/11 → 15/12/11

Access to Document

10.1109/CDC.2011.6160422

Cite this

@inproceedings{fd6c001700744c0c9c067a297abf9657,

title = "Linking hyperbolic and parabolic p.d.e.{\textquoteright}s",

abstract = "In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.{\textquoteright}s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain existence and uniqueness of solutions for the uniform elliptic p.d.e.{\textquoteright}s and for the Schrodinger equation.",

author = "Zwart, \{Heiko J.\} and \{Le Gorrec\}, Yann and Bernhard Maschke",

note = "It has the following IEEE Catalog Number: CFP11CDC-USB; 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, CDC-ECC ; Conference date: 12-12-2011 Through 15-12-2011",

year = "2011",

month = dec,

doi = "10.1109/CDC.2011.6160422",

language = "English",

isbn = "978-1-61284-800-6",

series = "IEEE Conference on Decision and Control and European Control Conference",

publisher = "IEEE",

pages = "4921--4924",

booktitle = "Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)",

address = "United States",

}

Zwart, HJ, Le Gorrec, Y & Maschke, B 2011, Linking hyperbolic and parabolic p.d.e.’s. in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). IEEE Conference on Decision and Control and European Control Conference, vol. 2011, IEEE, Piscataway, NJ, pp. 4921-4924, 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, USA, Florida, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160422

Linking hyperbolic and parabolic p.d.e.’s. / Zwart, Heiko J.; Le Gorrec, Yann; Maschke, Bernhard.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). Piscataway, NJ: IEEE, 2011. p. 4921-4924 (IEEE Conference on Decision and Control and European Control Conference; Vol. 2011).

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

TY - GEN

T1 - Linking hyperbolic and parabolic p.d.e.’s

AU - Zwart, Heiko J.

AU - Le Gorrec, Yann

AU - Maschke, Bernhard

N1 - Conference code: 50

PY - 2011/12

Y1 - 2011/12

N2 - In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.’s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain existence and uniqueness of solutions for the uniform elliptic p.d.e.’s and for the Schrodinger equation.

AB - In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.’s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain existence and uniqueness of solutions for the uniform elliptic p.d.e.’s and for the Schrodinger equation.

UR - http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc-2011/data/start.htm

U2 - 10.1109/CDC.2011.6160422

DO - 10.1109/CDC.2011.6160422

M3 - Conference contribution

SN - 978-1-61284-800-6

SN - 9978-1-4673-0457-3 (CD)

T3 - IEEE Conference on Decision and Control and European Control Conference

SP - 4921

EP - 4924

BT - Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)

PB - IEEE

CY - Piscataway, NJ

T2 - 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -

Linking hyperbolic and parabolic p.d.e.’s

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this