| Title:
|
Nonmonotone nonconvolution functions of positive type and applications (English) |
| Author:
|
Bárta, Tomáš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
211-220 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
functions of positive type |
| Keyword:
|
nonconvolution integral equation |
| Keyword:
|
chemically reacting viscoelastic fluid |
| MSC:
|
42A82 |
| MSC:
|
45A05 |
| MSC:
|
45M05 |
| MSC:
|
76A10 |
| idZBL:
|
Zbl 1265.42019 |
| idMR:
|
MR3017255 |
| . |
| Date available:
|
2012-08-08T08:58:41Z |
| Last updated:
|
2014-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142885 |
| . |
| Reference:
|
[1] Bárta T.: Global existence for a nonlinear model of 1D chemically reacting viscoelastic body.preprint, 2012. |
| Reference:
|
[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. Zbl 1182.35184, MR 2605756 |
| Reference:
|
[3] Cannarsa P., Sforza D.: Integro-differential equations of hyperbolic type with positive definite kernels.J. Differential Equations 250 (2011), no. 12, 4289–4335. Zbl 1218.45010, MR 2793256, 10.1016/j.jde.2011.03.005 |
| Reference:
|
[4] Gripenberg G., Londen S.O., Staffans O.: Volterra integral and functional equations.Encyclopedia of Mathematics and its Applications, 34, Cambridge University Press, Cambridge, 1990. Zbl 1159.45001, MR 1050319 |
| Reference:
|
[5] Halanay A.: On the asymptotic behavior of the solutions of an integro-differential equation.J. Math. Anal. Appl 10 (1965), 319–324. Zbl 0136.10202, MR 0176304, 10.1016/0022-247X(65)90126-5 |
| Reference:
|
[6] Kiffe T.: On nonlinear Volterra equations of nonconvolution type.J. Differential Equations 22 (1976), no. 2, 349–367. Zbl 0298.45003, MR 0417721, 10.1016/0022-0396(76)90033-4 |
| Reference:
|
[7] Mustapha K., McLean W.: Discontinuous Galerkin method for an evolution equation with a memory term of positive type.Math. Comp. 78 (2009), no. 268, 1975–1995. Zbl 1198.65195, MR 2521275, 10.1090/S0025-5718-09-02234-0 |
| Reference:
|
[8] Prüss J.: Evolutionary Integral Equations and Applications.Monographs in Mathematics, 87, Birkhäuser, Basel, 1993. MR 1238939 |
| Reference:
|
[9] Rajagopal K.R., Wineman A.S.: A note on viscoelastic materials that can age.International Journal of Non-Linear Mechanics 39 (2004), 1547–1554. 10.1016/j.ijnonlinmec.2003.09.001 |
| Reference:
|
[10] Rajagopal K.R., Wineman A.S.: Applications of viscoelastic clock models in biomechanics.Acta Mechanica 213 (2010), no. 3–4, 255–266. 10.1007/s00707-009-0262-4 |
| Reference:
|
[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. Zbl 0719.73013, MR 0919738 |
| Reference:
|
[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. Zbl 1129.74314, MR 2077662 |
| . |
