On a parabolic integrodifferential equation of Barbashin type
Commentationes Mathematicae Universitatis Carolinae (2011)
- Volume: 52, Issue: 3, page 391-401
- ISSN: 0010-2628
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topPachpatte, B. G.. "On a parabolic integrodifferential equation of Barbashin type." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 391-401. <http://eudml.org/doc/246187>.
@article{Pachpatte2011,
abstract = {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.},
author = {Pachpatte, B. G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {parabolic integrodifferential equation; Barbashin type; integral inequality; explicit estimate; approximate solutions; continuous dependence on parameters; parabolic integro-differential equation; integral inequality; approximate solution; Barbashin type; Gronwall type lemma; initial value problem; continuous dependence},
language = {eng},
number = {3},
pages = {391-401},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a parabolic integrodifferential equation of Barbashin type},
url = {http://eudml.org/doc/246187},
volume = {52},
year = {2011},
}
TY - JOUR
AU - Pachpatte, B. G.
TI - On a parabolic integrodifferential equation of Barbashin type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 3
SP - 391
EP - 401
AB - 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.
LA - eng
KW - parabolic integrodifferential equation; Barbashin type; integral inequality; explicit estimate; approximate solutions; continuous dependence on parameters; parabolic integro-differential equation; integral inequality; approximate solution; Barbashin type; Gronwall type lemma; initial value problem; continuous dependence
UR - http://eudml.org/doc/246187
ER -
References
top- 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. Zbl0949.45006MR1760093
- Barbashin E.A., On conditions for conservation of stability of solutions to integro-differential equations, (in Russian), Izv. VUZov Mat. 1 (1957), 25–34. MR0136958
- Corduneanu C., Integral Equations and Applications, Cambridge University Press, Cambridge, 1991. Zbl1156.45001MR1109491
- Pachpatte B.G., Inequalities for Differential and Integral Equations, Academic Press, New York, 1998. Zbl1032.26008MR1487077
- Pachpatte B.G., On mixed Volterra-Fredholm type integral equations, Indian J. Pure Appl. Math. 17 (1986), 488–496. Zbl0597.45012MR0840757
- Pachpatte B.G., On nonlinear coupled parabolic integrodifferential equations, J. Math. Phys. Sci. 21 (1987), 39–79. Zbl0624.45013MR0884095
- Pachpatte B.G., 10.1080/01630560802679265, Numer. Funct. Anal. Optim. 30 (2009), 136–147. Zbl1166.45005MR2492079DOI10.1080/01630560802679265
- Pachpatte B.G., On a nonlinear Volterra integral equation in two variables, Sarajevo J. Math. 6(19) (2010), 59–73. Zbl1204.45009MR2676610
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