Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Fokas's Unified Transform Method for linear systems


Authors: Bernard Deconinck, Qi Guo, Eli Shlizerman and Vishal Vasan
Journal: Quart. Appl. Math. 76 (2018), 463-488
DOI: https://doi.org/10.1090/qam/1484
Published electronically: September 28, 2017
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Abstract | References | Additional Information

Abstract: We demonstrate the use of the Unified Transform Method or Method of Fokas for boundary value problems for systems of constant-coefficient linear partial differential equations. We discuss how the apparent branch singularities typically appearing in the global relation are removable, as they arise symmetrically in the global relations. This allows the method to proceed, in essence, as for scalar problems. We illustrate the use of the method with boundary value problems for the Klein-Gordon equation and the linearized Fitzhugh-Nagumo system. Wave equations are treated separately in an appendix.


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Additional Information

Bernard Deconinck
Affiliation: Department of Applied Mathematics, University of Washington, Campus Box 353925, Seattle, WA, 98195
Email: deconinc@uw.edu

Qi Guo
Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095-1555
Email: qiguo@math.ucla.edu

Eli Shlizerman
Affiliation: Department of Applied Mathematics & Department of Electrical Engineering, University of Washington, Campus Box 353925, Seattle, WA, 98195
Email: shlizee@uw.edu

Vishal Vasan
Affiliation: International Centre for Theoretical Sciences, Bengaluru, India
Email: vishal.vasan@icts.res.in

DOI: https://doi.org/10.1090/qam/1484
Received by editor(s): April 28, 2017
Received by editor(s) in revised form: August 10, 2017
Published electronically: September 28, 2017
Article copyright: © Copyright 2017 Brown University

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