AffiliationDepartment of Mathematics, University of Arizona
MetadataShow full item record
PublisherSpringer Science and Business Media LLC
CitationBramburger, J. J., & Henderson, C. (2021). The speed of traveling waves in a FKPP-Burgers system. Archive for Rational Mechanics and Analysis, 1-39.
Rights© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature (2021)
Collection InformationThis 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 firstname.lastname@example.org.
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.
Note12 month embargo; published: 26 May 2021
VersionFinal accepted manuscript
SponsorsDivision of Mathematical Sciences