| Title:
|
On a parabolic integrodifferential equation of Barbashin type (English) |
| Author:
|
Pachpatte, B. G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
391-401 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we study some basic qualitative properties of solutions of a nonlinear parabolic integrodifferential equation of Barbashin type which occurs frequently in applications. The fundamental integral inequality with explicit estimate is used to establish the results. (English) |
| Keyword:
|
parabolic integrodifferential equation |
| Keyword:
|
Barbashin type |
| Keyword:
|
integral inequality |
| Keyword:
|
explicit estimate |
| Keyword:
|
approximate solutions |
| Keyword:
|
continuous dependence on parameters |
| MSC:
|
34K10 |
| MSC:
|
35R10 |
| idZBL:
|
Zbl 1249.45014 |
| idMR:
|
MR2843231 |
| . |
| Date available:
|
2011-08-15T19:17:48Z |
| Last updated:
|
2013-10-14 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141610 |
| . |
| Reference:
|
[1] Appell J.M., Kalitvin A.S., Zabrejko P.P.: Partial integral operators and integro-differential equations.Pure and Applied Mathematics Monographs, 230, Marcel Dekker, New York, 2000. Zbl 0949.45006, MR 1760093 |
| Reference:
|
[2] Barbashin E.A.: On conditions for conservation of stability of solutions to integro-differential equations.(in Russian), Izv. VUZov Mat. 1 (1957), 25–34. MR 0136958 |
| Reference:
|
[3] Corduneanu C.: Integral Equations and Applications.Cambridge University Press, Cambridge, 1991. Zbl 1156.45001, MR 1109491 |
| Reference:
|
[4] Pachpatte B.G.: Inequalities for Differential and Integral Equations.Academic Press, New York, 1998. Zbl 1032.26008, MR 1487077 |
| Reference:
|
[5] Pachpatte B.G.: On mixed Volterra-Fredholm type integral equations.Indian J. Pure Appl. Math. 17 (1986), 488–496. Zbl 0597.45012, MR 0840757 |
| Reference:
|
[6] Pachpatte B.G.: On nonlinear coupled parabolic integrodifferential equations.J. Math. Phys. Sci. 21 (1987), 39–79. Zbl 0624.45013, MR 0884095 |
| Reference:
|
[7] Pachpatte B.G.: On a parabolic type Fredholm integrodifferential equation.Numer. Funct. Anal. Optim. 30 (2009), 136–147. Zbl 1166.45005, MR 2492079, 10.1080/01630560802679265 |
| Reference:
|
[8] Pachpatte B.G.: On a nonlinear Volterra integral equation in two variables.Sarajevo J. Math. 6(19) (2010), 59–73. Zbl 1204.45009, MR 2676610 |
| . |
