Journal of Evolution Equations

, Volume 6, Issue 1, pp 1–28

Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces

  • Allaberen Ashyralyev
Original Paper

DOI: 10.1007/s00028-005-0194-y

Cite this article as:
Ashyralyev, A. J. evol. equ. (2006) 6: 1. doi:10.1007/s00028-005-0194-y

Abstract.

The well-posedness of the nonlocal boundary-value problem for abstract parabolic differential equations in Bochner spaces is established. The first and second order of accuracy difference schemes for the approximate solutions of this problem are considered. The coercive inequalities for the solutions of these difference schemes are established. In applications, the almost coercive stability and coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary-value problem for parabolic equation are obtained.

Mathematics Subject Classification (2000).

65N47D34B

Key words.

Parabolic equationNonlocal boundary-value problemDifference schemesWell-posednessCoercive inequalities

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Allaberen Ashyralyev
    • 1
  1. 1.Department of MathematicsFatih UniversityIstanbulTurkey