Differential Equations with Constraints
(2009)- Abstract
- We study various differential equations subject to constraints. In the first part we study a partial differential
equation, Burgers equation, subject to time-periodicity constraint. The forcing term is time-periodic and may be
highly irregular. We prove an existence and uniqueness result which in a sense is optimal since we show that the
operator corresponding to the Burgers equation is a diffeomorphism from a functional space to its dual.
In the second part we study general ordinary differential equations subject to general constraints. We first
describe precisely what the index is. Subsequently we investigate the particular case of linear ordinary
differential equation and... (More) - We study various differential equations subject to constraints. In the first part we study a partial differential
equation, Burgers equation, subject to time-periodicity constraint. The forcing term is time-periodic and may be
highly irregular. We prove an existence and uniqueness result which in a sense is optimal since we show that the
operator corresponding to the Burgers equation is a diffeomorphism from a functional space to its dual.
In the second part we study general ordinary differential equations subject to general constraints. We first
describe precisely what the index is. Subsequently we investigate the particular case of linear ordinary
differential equation and derive a new normal form. We show that it is characterized by defect indices and we
show the relation with the Kronecker normal form. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1396748
- author
- Verdier, Olivier LU
- supervisor
- opponent
-
- Professor Reich, Sebastian, Potsdam University, Germany
- organization
- publishing date
- 2009
- type
- Thesis
- publication status
- published
- subject
- pages
- 127 pages
- publisher
- Centre for Mathematical Sciences, Lund University
- defense location
- Lecture hall MH:C, Centre for Mathematical Sciences, Sölvegatan 18, Faculty of Engineering Lund University
- defense date
- 2009-06-12 13:15:00
- ISBN
- 978-91-628-7812-2
- language
- English
- LU publication?
- yes
- id
- 5a1b4f4d-f7d3-4c01-837f-113f38c824ec (old id 1396748)
- date added to LUP
- 2016-04-04 10:12:09
- date last changed
- 2018-11-21 20:57:24
@phdthesis{5a1b4f4d-f7d3-4c01-837f-113f38c824ec,
abstract = {{We study various differential equations subject to constraints. In the first part we study a partial differential <br/><br>
equation, Burgers equation, subject to time-periodicity constraint. The forcing term is time-periodic and may be <br/><br>
highly irregular. We prove an existence and uniqueness result which in a sense is optimal since we show that the <br/><br>
operator corresponding to the Burgers equation is a diffeomorphism from a functional space to its dual. <br/><br>
In the second part we study general ordinary differential equations subject to general constraints. We first <br/><br>
describe precisely what the index is. Subsequently we investigate the particular case of linear ordinary <br/><br>
differential equation and derive a new normal form. We show that it is characterized by defect indices and we <br/><br>
show the relation with the Kronecker normal form.}},
author = {{Verdier, Olivier}},
isbn = {{978-91-628-7812-2}},
language = {{eng}},
publisher = {{Centre for Mathematical Sciences, Lund University}},
school = {{Lund University}},
title = {{Differential Equations with Constraints}},
url = {{https://lup.lub.lu.se/search/files/5486348/1396749.pdf}},
year = {{2009}},
}