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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 9, Pages 469-478
http://dx.doi.org/10.1155/S0161171204203441

Method of semidiscretization in time for quasilinearintegrodifferential equations

Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur 208 016, India

Received 1 March 2001

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a class of quasilinear integrodifferential equations in a reflexive Banach space. We apply the method of semidiscretization in time to establish the existence, uniqueness, and continuous dependence on the initial data of strong solutions.