Well-Posedness of Parabolic Difference Equations

  • A. Ashyralyev
  • P. E. Sobolevskii

Part of the Operator Theory Advances and Applications book series (OT, volume 69)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. A. Ashyralyev, P. E. Sobolevskii
    Pages 1-69
  3. A. Ashyralyev, P. E. Sobolevskii
    Pages 71-156
  4. A. Ashyralyev, P. E. Sobolevskii
    Pages 157-240
  5. A. Ashyralyev, P. E. Sobolevskii
    Pages 241-326
  6. Back Matter
    Pages 327-353

About this book


A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.


Boundary value problem differential equation functional analysis mathematical physics partial differential equation

Authors and affiliations

  • A. Ashyralyev
    • 1
  • P. E. Sobolevskii
    • 2
  1. 1.Department of Mathematical AnalysisThe Turkmen State UniversityAshgabatTurkmenistan
  2. 2.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael

Bibliographic information