rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Summation of the spectral expansions associated with the solvability of the heat and wave problems
  name:
    name part: Akter, Fargana
    role:
      role term: creator
    role:
      role term: author
  name:
    name part: Abdumalik Rakhimov
    role:
      role term: degree supervisor
  name:
    name part: Ahsan Ali Khan
    role:
      role term: degree supervisor
  name:
    name part: International Islamic University Malaysia
    name part: Kulliyyah of Engineering
  genre: Theses, IIUM local
  origin info: issuance
  physical description:
    extent: xix, 100 leaves : illustrations ; 30cm.
  abstract: A relation between the theory of multiple Fourier series and partial differential equations was divulged in the beginning of the nineteenth century and it is known as spectral theory of the differential operators. The spectral theory of the differential operators is a significant part of mathematical sciences and it has applications in many branches of engineering. The development of the spectral theory of the differential operator is started since the time when Fourier studied heat conduction problem in a rod and the solution is found as a form of sin series. To adjust the obtained solution leads to study of the problems of the convergence of that series solutions and it depends on the initial and/or boundary data. Obtained series solutions of the problems may not be convergent. Then the problem of summability will occur. Regularization of the divergent series solution is accurate numerical interpretations of the solutions of the problems. In this research, to find the equiconvergence of the spectral expansions and to find the solution of the heat and wave problem regularization was required. In the first phase, we studied a special elliptic partial sum of order 2(m+1) of multiple Fourier series and integral in the spaces of singular distributions. We discussed the equiconvergence in summation of the Fourier series and integral of the linear continuous functional for specific conditions in the Lioville space. Therefore, we proved a precise equiconvergence relation between index of the Bochner-Riesz means of the expansions and power of the singularity of the distributions with compact support in summation associated with the elliptic operator. After that, we studied the vibration problem made of thin elastic membrane stretched tightly over a square frame. The deflection of the membrane during the motion is small compared to the size of the membrane. And for heat transfer problems the plate is made of some thermally conductive material. We discussed different types o…
  note: by Fargana Akter
  note: Abstracts in English and Arabic.
  note: "A thesis submitted in fulfilment of the requirement for the degree of Doctor of Philosophy (Engineering)." --On title page.
  note: Thesis (Ph.D)--International Islamic University Malaysia, 2020.
  note: Includes bibliographical references (leaves 90-99).
  subject:
    topic: Wavelets (Mathematics)
  subject:
    topic: Fourier series
  subject:
    topic: Differential equations, Partial
  identifier: http://studentrepo.iium.edu.my/handle/123456789/10095
  record info:
    record content source: UIAM
    language of cataloging:
      language term: eng