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

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  • Okan Gercek

Abstract

A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem −d2u(t)/dt2 + sign(t)Au(t) = g(t), (0 ≤ t ≤ 1), du(t)/dt + sign(t)Au(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.

Suggested Citation

  • Okan Gercek, 2012. "Well‐Posedness of the First Order of Accuracy Difference Scheme for Elliptic‐Parabolic Equations in Hölder Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:237657
    DOI: 10.1155/2012/237657
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    References listed on IDEAS

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    1. Allaberen Ashyralyev & Okan Gercek, 2010. "On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-17, July.
    2. Allaberen Ashyralyev & Okan Gercek, 2010. "On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic‐Parabolic Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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