Abstract and Applied Analysis

Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces

Okan Gercek

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Abstract

A first order of accuracy difference scheme for theapproximate 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 normsfor the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 237657, 12 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174070

Digital Object Identifier
doi:10.1155/2012/237657

Mathematical Reviews number (MathSciNet)
MR2970010

Zentralblatt MATH identifier
1253.35083

Citation

Gercek, Okan. Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 237657, 12 pages. doi:10.1155/2012/237657. https://projecteuclid.org/euclid.aaa/1365174070


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