Abstract
In this paper, we study the existence and uniqueness of a weak solution for a delay integrodifferential parabaolic equation using the method of semidiscretization.
Similar content being viewed by others
References
Bahuguna, D., Raghavendra, V.: Rothe’s method to parabolic integrodifferential equation via abstract integrodifferential equations. Appl. Anal. 33(3–4), 153–167 (1989)
Bahuguna, D., Pani, A.K., Raghavendra, A.K.: Rothe’s method to semilinear hyperbolic integrodifferential equations. J. Appl. Math. Stoch. Anal. 3(4), 245–252 (1990)
Bouziani, A., Mechri, R.: The Rothe’s method to a parabolic integrodifferential equation with a nonclassical boundary conditions. Int. J. Stoch. Anal. Art. ID 519684, 16 (2010)
Kacur J.: Method of Rothe in evolution equations. Equadiff 6, Proceedings of the international conference on differential equations and their applications, pp. 23–34 (1985)
Kikuchi, N., Kacur, J.: Convergence of Rothe’s method in H\(\ddot{{{\rm o}}}\)lder spaces. Appl. Math. 48(5), 353–365 (2003)
Lakoud, A.G., Chaoni, A.: Rothe’s method applied to semilinear hyperbolic integro-differential equation with integral conditions. Int. J. Open Probl. Comput. Sci. Math. 4(1), 1–14 (2011).
Rektorys, K.: On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables. Czechoslov. Math. J. 21(96), 318–339 (1971)
Rektorys, K.: The Method of Discretization in Time and Partial Differential Equations. D. Reidel Publishing Company, Dordrecht (1982)
Rektorys, K.: Numerical and theoretical treating of evolution problems by the method of discretization in time. Proceedings of the international conference on differential equations and their applications, pp. 71–84 (1985)
Acknowledgments
The authors thank the referee for his valuable suggestions. The first author acknowledges the sponsorship from CSIR, India, under its Research Grant 09/092(0652)/2008-EMR-1. The second author acknowledges the financial help from the Department of Science and Technology, New Delhi, under its research project SR/S4/MS:796/12.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Raheem, A., Bahuguna, D. A Study of Delay Integrodifferential Parabolic Problems. Differ Equ Dyn Syst 21, 309–321 (2013). https://doi.org/10.1007/s12591-013-0166-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12591-013-0166-6