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Computer Assisted Proofs in Dissipative Partial Differential Equations

Computer Assisted Proofs in Dissipative Partial Differential Equations
File Size:
126.14 kB
Author:
Jacek Cyranka
Email:
jacek[dot]cyranka[at]ii[dot]uj[dot]edu[dot]pl
Date:
14 August 2013
Downloads:
9 x

 

Abstract: The goal of this paper is to present a brief survey of our research that has focused on studying the dynamics of dissipative partial diff erential equations by performing computer as sisted proofs. We provide a description of the main ideas behind the computer assisted proofs that we have performed, along with related topics. Th e emphasis is given to the case of the vis cous Burgers equation with constant forcing, for which the existence of globally attracting fixed points has been established. To achieve this goal, we used a combination of analytical results with computer assistance.

Keywords: rigorous numerics, Lohner algorithm, viscous Burgers equation, dissipative partial diff erential equation, interval arithmetic

Area: Applied Mathematics

BibTeX:

@article{Cyrank2012,
  author = {Jacek Cyranka},
  title = {Computer Assisted Proofs in Dissipative Partial Differential Equations},
  journal = {Challenges of Modern Technology},
  year = {2012},
  volume = {3},
  number = {3},
  pages = {3--6},
  url = {http://www.journal.young-scientists.eu/index.php/isuues/file/95-computer-assisted-proofs-in-dissipative-partial-differential-equations}
}
 
 

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