Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 904824, 16 pages
Nonlocal Boundary Value Problems for Elliptic-Parabolic Differential and Difference Equations
1Department of Mathematics, Fatih University, 34500 Buyukcekmece, Istanbul, Turkey
2Vocational School, Fatih University, 34500 Buyukcekmece, Istanbul, Turkey
Received 30 June 2008; Accepted 17 September 2008
Academic Editor: Yong Zhou
Copyright © 2008 Allaberen Ashyralyev and Okan Gercek. 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 abstract nonlocal boundary value problem
for differential equations in a Hilbert space with the self-adjoint positive definite
operator is considered. The well-posedness of this problem in Hölder spaces with
a weight is established. The coercivity inequalities for the solution of boundary value
problems for elliptic-parabolic equations are obtained. The first order of accuracy difference
scheme for the approximate solution of this nonlocal boundary value problem
is presented. The well-posedness of this difference scheme in Hölder spaces is established.
In applications, coercivity inequalities for the solution of a difference scheme
for elliptic-parabolic equations are obtained.