A Generalized Method for A Posteriori and A Priori Error Estimates for Homoclinic Orbits in Reversible Systems
Jankovic, Sally
2023-05
Loading...
View/Download File
Persistent link to this item
Statistics
View StatisticsJournal Title
Journal ISSN
Volume Title
Title
A Generalized Method for A Posteriori and A Priori Error Estimates for Homoclinic Orbits in Reversible Systems
Authors
Published Date
2023-05
Publisher
Type
Thesis or Dissertation
Abstract
Coherent structures in pattern-forming systems, such as pulses and spikes, are often mathematically represented as homoclinic orbits. We here present a generalized method for finding such homoclinic solutions to 2nd-order ODEs using a posteriori data derived from approximate solutions to boundary value problems on truncated intervals. We then show in the opposite direction that the a priori existence of a non-degenerate homoclinic implies the existence of a family of solutions to a Dirichlet boundary-value problem, with an explicit lower bound on domain size necessary to obtain a solution. In each direction, we also provide explicit error estimates as a function of truncation error. We lastly apply our method to find a family of homoclinics in the Lengyel-Epstein system and compute a minimum domain size for the existence of finite-domain solutions using the a priori proof.
Description
University of Minnesota Ph.D. dissertation. May 2023. Major: Mathematics. Advisor: Arnd Scheel. 1 computer file (PDF); vi, 80 pages + 1 compressed folder of supplementary files.
Related to
Replaces
License
Collections
Series/Report Number
Funding information
Isbn identifier
Doi identifier
Previously Published Citation
Suggested citation
Jankovic, Sally. (2023). A Generalized Method for A Posteriori and A Priori Error Estimates for Homoclinic Orbits in Reversible Systems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/257125.
Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.