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Coercive solvability of the nonlocal boundary value problem for parabolic differential equations

Author

Listed:
  • A. Ashyralyev
  • A. Hanalyev
  • P. E. Sobolevskii

Abstract

The nonlocal boundary value problem, v ′ ( t ) + A v ( t ) = f ( t ) ( 0 ≤ t ≤ 1 ) , v ( 0 ) = v ( λ ) + μ ( 0 < λ ≤ 1 ) , in an arbitrary Banach space E with the strongly positive operator A , is considered. The coercive stability estimates in Hölder norms for the solution of this problem are proved. The exact Schauder's estimates in Hölder norms of solutions of the boundary value problem on the range { 0 ≤ t ≤ 1 , x ℝ n } for 2 m -order multidimensional parabolic equations are obtaine.

Suggested Citation

  • A. Ashyralyev & A. Hanalyev & P. E. Sobolevskii, 2001. "Coercive solvability of the nonlocal boundary value problem for parabolic differential equations," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-9, January.
    • Handle: RePEc:hin:jnlaaa:436047
    DOI: 10.1155/S1085337501000495
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    Cited by:

    1. Charyyar Ashyralyyev & Oznur Demirdag, 2012. "The Difference Problem of Obtaining the Parameter of a Parabolic Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Allaberen Ashyralyev & Yasar Sozen & Pavel E. Sobolevskii, 2007. "A Note on the Parabolic Differential and Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2007(1).
    3. 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).
    4. Xiuling Yin & Yanqin Liu, 2014. "Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. F. Zouyed & F. Rebbani & N. Boussetila, 2007. "On a Class of Multitime Evolution Equations with Nonlocal Initial Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2007(1).
    6. Charyyar Ashyralyyev & Ayfer Dural & Yasar Sozen, 2012. "Finite Difference Method for the Reverse Parabolic Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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