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Second Order Equations in Functional Spaces: Qualitative and Discrete Well‐Posedness

Author

Listed:
  • A. Ashyralyev
  • J. Pastor
  • S. Piskarev
  • H. A. Yurtsever

Abstract

The present survey contains the recent results on the local and nonlocal well‐posed problems for second order differential and difference equations. Results on the stability of differential problems for second order equations and of difference schemes for approximate solution of the second order problems are presented.

Suggested Citation

  • A. Ashyralyev & J. Pastor & S. Piskarev & H. A. Yurtsever, 2015. "Second Order Equations in Functional Spaces: Qualitative and Discrete Well‐Posedness," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:948321
    DOI: 10.1155/2015/948321
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    References listed on IDEAS

    as
    1. Allaberen Ashyralyev & Ozgur Yildirim, 2012. "A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-29, September.
    2. Allaberen Ashyralyev & Ozgur Yildirim, 2013. "On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self-Adjoint Operator," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, December.
    3. Allaberen Ashyralyev & Ozgur Yildirim, 2012. "A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Allaberen Ashyralyev & Ozgur Yildirim, 2013. "On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self‐Adjoint Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. A. Ashyralyev & P. E. Sobolevskii, 2001. "A note on the difference schemes for hyperbolic equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 6(2), pages 63-70.
    6. A. Ashyralyev & G. Judakova & P. E. Sobolevskii, 2006. "A note on the difference schemes for hyperbolic‐elliptic equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
    7. B. Eberhardt & G. Greiner, 1992. "Baillon’s Theorem on Maximal Regularity," Springer Books, in: C. B. Huijsmans & W. A. J. Luxemburg (ed.), Positive Operators and Semigroups on Banach Lattices, pages 47-54, Springer.
    8. Yildirim Ozdemir & Mehmet Kucukunal, 2012. "A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. Yildirim Ozdemir & Mehmet Kucukunal, 2012. "A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, June.
    10. A. Ashyralyev & G. Judakova & P. E. Sobolevskii, 2006. "A note on the difference schemes for hyperbolic-elliptic equations," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-13, February.
    11. A. Ashyralyev & P. E. Sobolevskii, 2001. "A note on the difference schemes for hyperbolic equations," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-8, January.
    12. Necmettin Aggez & Maral Ashyralyyewa, 2012. "Numerical Solution of Stochastic Hyperbolic Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    13. Necmettin Aggez & Maral Ashyralyyewa, 2012. "Numerical Solution of Stochastic Hyperbolic Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, August.
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