On uniqueness for bounded channel flows of viscoelastic fluids
Marshall J. Leitman; Epifanio G. Virga
- Volume: 82, Issue: 4, page 717-723
- ISSN: 1120-6330
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topLeitman, Marshall J., and Virga, Epifanio G.. "On uniqueness for bounded channel flows of viscoelastic fluids." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.4 (1988): 717-723. <http://eudml.org/doc/287316>.
@article{Leitman1988,
abstract = {It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function $G$ is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming $G$ to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.},
author = {Leitman, Marshall J., Virga, Epifanio G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Uniqueness; Channel flows; Viscoelasticy fluids; bounded channel flow; viscoelastic fluid; stress relaxation function},
language = {eng},
month = {12},
number = {4},
pages = {717-723},
publisher = {Accademia Nazionale dei Lincei},
title = {On uniqueness for bounded channel flows of viscoelastic fluids},
url = {http://eudml.org/doc/287316},
volume = {82},
year = {1988},
}
TY - JOUR
AU - Leitman, Marshall J.
AU - Virga, Epifanio G.
TI - On uniqueness for bounded channel flows of viscoelastic fluids
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/12//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 4
SP - 717
EP - 723
AB - It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function $G$ is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming $G$ to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.
LA - eng
KW - Uniqueness; Channel flows; Viscoelasticy fluids; bounded channel flow; viscoelastic fluid; stress relaxation function
UR - http://eudml.org/doc/287316
ER -
References
top- LEITMAN, M.J. and VIRGA, E.G. (1988) - On bounded channel flows of viscoelastic fluids, «Atti Acc. Lincei Rend. fis.», 82,291-291. Zbl0714.76013MR1152648
- CAPRIZ, G. and VIRGA, E.G. (1988) - Un teorema di unicità in viscoelasticità lineare, «Rend. Sem. Mat. Univ. Padova», 79, 15-24. Zbl0655.73020MR964016
- VERGARA CAFFARELLI, G. and VIRGA, E.G. (1987) - Sull'unicità della soluzione del problema dinamico della viscoelasticità lineare, «Atti Acc. Lincei Rend. fis.», 81, 379-387. Zbl0667.73027MR999829
- JOSEPH, D.D., RENARDY, M. and SAUT, J.C. (1984-85) - Hyperbolicity and change of type in the flow of viscoelastic fluids, «Arch. Rational Mech. Anal.», 87, 213-251. Zbl0572.76011MR768067DOI10.1007/BF00250725
- HALE, J. (1971) - Functional differential equations, «Springer Verlag, Berlin», etc. Zbl0222.34003MR390425
- LEITMAN, M.J. and MIZEL, V.J. (1974) - On fading memory spaces and hereditary integral equations, «Arch. Rational Mech. Anal.», 75, 18-51. Zbl0297.45001MR367734
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