Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces. (16th September 2012)

• Record Type: Journal Article
• Authors: Gercek, Okan
• Other Names: Ashyralyev Allaberen Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-09-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/237657
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem − d 2 u ( t ) / d t 2 + sign ( t ) A u ( t ) = g ( t ), ( 0 ≤ t ≤ 1 ), d u ( t ) / d t + sign ( t ) A u ( t ) = f ( t ), ( − 1 ≤ t ≤ 0 ), u ( 0 + ) = u ( 0 − ), u ′ ( 0 + ) = u ′ ( 0 − ), and u ( 1 ) = u ( − 1 ) + μ for differential equations in a Hilbert space H with a self-adjoint positive definite operator A is considered. The well-posedness of this difference scheme in Hölder spaces without a weight is established. Moreover, as applications, coercivity estimates in Hölder norms for the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained.