Nonmonotone nonconvolution functions of positive type and applications

Tomáš Bárta

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 2, page 211-220
  • ISSN: 0010-2628

Abstract

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We present two sufficient conditions for nonconvolution kernels to be of positive type. We apply the results to obtain stability for one-dimensional models of chemically reacting viscoelastic materials.

How to cite

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Bárta, Tomáš. "Nonmonotone nonconvolution functions of positive type and applications." Commentationes Mathematicae Universitatis Carolinae 53.2 (2012): 211-220. <http://eudml.org/doc/246789>.

@article{Bárta2012,
abstract = {We present two sufficient conditions for nonconvolution kernels to be of positive type. We apply the results to obtain stability for one-dimensional models of chemically reacting viscoelastic materials.},
author = {Bárta, Tomáš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {functions of positive type; nonconvolution integral equation; chemically reacting viscoelastic fluid; functions of positive type; nonconvolution integral equation; chemically reacting viscoelastic fluid},
language = {eng},
number = {2},
pages = {211-220},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Nonmonotone nonconvolution functions of positive type and applications},
url = {http://eudml.org/doc/246789},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Bárta, Tomáš
TI - Nonmonotone nonconvolution functions of positive type and applications
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 2
SP - 211
EP - 220
AB - We present two sufficient conditions for nonconvolution kernels to be of positive type. We apply the results to obtain stability for one-dimensional models of chemically reacting viscoelastic materials.
LA - eng
KW - functions of positive type; nonconvolution integral equation; chemically reacting viscoelastic fluid; functions of positive type; nonconvolution integral equation; chemically reacting viscoelastic fluid
UR - http://eudml.org/doc/246789
ER -

References

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  1. Bárta T., Global existence for a nonlinear model of 1D chemically reacting viscoelastic body, preprint, 2012. 
  2. Bulíček M., Málek J., Rajagopal K.R., Mathematical results concerning unsteady flows of chemically reacting incompressible fluids, (English summary) Partial differential equations and fluid mechanics, 2653, London Math. Soc. Lecture Note Ser., 364, Cambridge Univ. Press, Cambridge, 2009. Zbl1182.35184MR2605756
  3. Cannarsa P., Sforza D., 10.1016/j.jde.2011.03.005, J. Differential Equations 250 (2011), no. 12, 4289–4335. Zbl1218.45010MR2793256DOI10.1016/j.jde.2011.03.005
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  7. Mustapha K., McLean W., 10.1090/S0025-5718-09-02234-0, Math. Comp. 78 (2009), no. 268, 1975–1995. Zbl1198.65195MR2521275DOI10.1090/S0025-5718-09-02234-0
  8. Prüss J., Evolutionary Integral Equations and Applications, Monographs in Mathematics, 87, Birkhäuser, Basel, 1993. MR1238939
  9. Rajagopal K.R., Wineman A.S., 10.1016/j.ijnonlinmec.2003.09.001, International Journal of Non-Linear Mechanics 39 (2004), 1547–1554. DOI10.1016/j.ijnonlinmec.2003.09.001
  10. Rajagopal K.R., Wineman A.S., 10.1007/s00707-009-0262-4, Acta Mechanica 213 (2010), no. 3–4, 255–266. DOI10.1007/s00707-009-0262-4
  11. Renardy M., Hrusa W.J., Nohel J.A., Mathematical problems in viscoelasticity, Pitman Monographs and Surveys in Pure and Applied Mathematics, 35, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. Zbl0719.73013MR0919738
  12. Tatar N.-E., Long time behavior for a viscoelastic problem with a positive definite kernel, Aust. J. Math. Anal. Appl. 1 (2004), no. 1, Art. 5, 11 pp. Zbl1129.74314MR2077662

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