On the solution of a hyperbolic one-dimensional free boundary problem for a Maxwell fluid
type: Item
instance of: scholarly article
title: On the solution of a hyperbolic one-dimensional free boundary problem for a Maxwell fluid
zbMATH Open document ID: 1342.35458
DOI: 10.1155/2011/606757
author: Lorenzo Fusi
author: Angiolo Farina
published in: Advances in Mathematical Physics
publication date: 2012-03-08T00:00:00Z
review text: Summary: We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of the authors [Far East J. Appl. Math. 52, No. 1, 43--80 (2011; Zbl 1230.35146)]. The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 6012966
Wikidata QID: Q58654850
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/606757
OpenAlex ID: W2158827792
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description: scientific article; zbMATH DE number 6012966