Article
Keywords:
parabolic integrodifferential equation; Barbashin type; integral inequality; explicit estimate; approximate solutions; continuous dependence on parameters
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.
References:
[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.
MR 1760093 |
Zbl 0949.45006
[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
[3] Corduneanu C.:
Integral Equations and Applications. Cambridge University Press, Cambridge, 1991.
MR 1109491 |
Zbl 1156.45001
[4] Pachpatte B.G.:
Inequalities for Differential and Integral Equations. Academic Press, New York, 1998.
MR 1487077 |
Zbl 1032.26008
[5] Pachpatte B.G.:
On mixed Volterra-Fredholm type integral equations. Indian J. Pure Appl. Math. 17 (1986), 488–496.
MR 0840757 |
Zbl 0597.45012
[6] Pachpatte B.G.:
On nonlinear coupled parabolic integrodifferential equations. J. Math. Phys. Sci. 21 (1987), 39–79.
MR 0884095 |
Zbl 0624.45013
[8] Pachpatte B.G.:
On a nonlinear Volterra integral equation in two variables. Sarajevo J. Math. 6(19) (2010), 59–73.
MR 2676610 |
Zbl 1204.45009