Abstract and Applied Analysis
Volume 2007 (2007), Article ID 61659, 16 pages
A Note on the Parabolic Differential and Difference Equations
1Department of Mathematics, Fatih University, Istanbul 34500, Turkey
2Institute of Mathematics, Hebrew University, 91904 Jerusalem, Israel
3Universidade Federal do Ceará, Ceará 60020, Brazil
Received 13 August 2006; Revised 12 December 2006; Accepted 6 March 2007
Academic Editor: Martin J. Bohner
Copyright © 2007 Allaberen Ashyralyev et al. 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.
The differential equation in a general Banach space with the strongly positive operator is ill-posed in the Banach space with norm . In the present paper, the well-posedness of this equation in the Hölder space with norm ), , is established. The almost coercivity inequality for solutions of the Rothe
difference scheme in spaces is proved. The well-posedness of this difference scheme in spaces is obtained.