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Differential Equations with Constraints

Verdier, Olivier LU (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:
author
supervisor
opponent
  • Professor Reich, Sebastian, Potsdam University, Germany
organization
publishing date
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
ISBN
978-91-628-7812-2
language
English
LU publication?
yes
id
5a1b4f4d-f7d3-4c01-837f-113f38c824ec (old id 1396748)
date added to LUP
2009-05-15 14:38:28
date last changed
2016-09-19 08:45:03
@misc{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},
  pages        = {127},
  publisher    = {ARRAY(0xb385ba8)},
  title        = {Differential Equations with Constraints},
  year         = {2009},
}