Show simple item record

dc.contributor.authorBramburger, Jason J.
dc.contributor.authorHenderson, Christopher
dc.date.accessioned2021-06-10T01:21:03Z
dc.date.available2021-06-10T01:21:03Z
dc.date.issued2021-05-26
dc.identifier.citationBramburger, J. J., & Henderson, C. (2021). The speed of traveling waves in a FKPP-Burgers system. Archive for Rational Mechanics and Analysis, 1-39.en_US
dc.identifier.issn0003-9527
dc.identifier.doi10.1007/s00205-021-01660-5
dc.identifier.urihttp://hdl.handle.net/10150/659850
dc.description.abstractWe consider a coupled reaction–advection–diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as a one-dimensional version of a model for a reacting fluid in which the arising density differences induce a buoyancy force advecting the fluid. We study front propagation in this system through the lens of traveling waves solutions. We are able to show two quite different behaviors depending on whether the coupling constant ρ is large or small. First, it is proved that there is a threshold ρ under which the advection has no effect on the speed of traveling waves (although the advection is nonzero). Second, when ρ is large, wave speeds must be at least O(ρ1 / 3). These results together give that there is a transition from pulled to pushed waves as ρ increases. Because of the complex dynamics involved in this and similar models, this is one of the first precise results in the literature on the effect of the coupling on the traveling wave solution. We use a mix of ordinary and partial differential equation methods in our analytical treatment, and we supplement this with a numerical treatment featuring newly created methods to understand the behavior of the wave speeds. Finally, various conjectures and open problems are formulated. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.en_US
dc.description.sponsorshipDivision of Mathematical Sciencesen_US
dc.language.isoenen_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.rights© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature (2021)en_US
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en_US
dc.titleThe Speed of Traveling Waves in a FKPP-Burgers Systemen_US
dc.typeArticleen_US
dc.identifier.eissn1432-0673
dc.contributor.departmentDepartment of Mathematics, University of Arizonaen_US
dc.identifier.journalArchive for Rational Mechanics and Analysisen_US
dc.description.note12 month embargo; published: 26 May 2021en_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal accepted manuscripten_US
dc.identifier.pii1660
dc.source.journaltitleArchive for Rational Mechanics and Analysis


Files in this item

Thumbnail
Name:
FKPP_Burgers.pdf
Embargo:
2022-05-26
Size:
652.0Kb
Format:
PDF
Description:
Final Accepted Manuscript

This item appears in the following Collection(s)

Show simple item record