Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Balanced flux formulations for multidimensional Evans-function computations for viscous shocks


Authors: Blake Barker, Jeffrey Humpherys, Gregory Lyng and Kevin Zumbrun
Journal: Quart. Appl. Math. 76 (2018), 531-545
MSC (2010): Primary 35Q35, 76L05, 35Pxx
DOI: https://doi.org/10.1090/qam/1492
Published electronically: October 25, 2017
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Abstract: The Evans function is a powerful tool for the stability analysis of viscous shock profiles; zeros of this function carry stability information. In the one-dimensional case, it is typical to compute the Evans function using Goodman's integrated coordinates (1986); this device facilitates the search for zeros of the Evans function by winding number arguments. Although integrated coordinates are not available in the multidimensional case, we show here that there is a choice of coordinates which gives similar advantages.


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Additional Information

Blake Barker
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84603
Email: blake@math.byu.edu

Jeffrey Humpherys
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84603
Email: jeffh@math.byu.edu

Gregory Lyng
Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071
Email: glyng@uwyo.edu

Kevin Zumbrun
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: kzumbrun@indiana.edu

DOI: https://doi.org/10.1090/qam/1492
Received by editor(s): March 6, 2017
Received by editor(s) in revised form: September 21, 2017
Published electronically: October 25, 2017
Additional Notes: The first author was partially supported by NSF grant DMS-0801745.
The second author was partially supported by NSF grant DMS-0847074 (CAREER)
The third author was partially supported by NSF grants DMS-0845127 (CAREER) and DMS-1413273
The last author was partially supported by NSF grant DMS-0801745
Article copyright: © Copyright 2017 Brown University

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