Rybalko A. 3. Homogenization of differential forms on manifolds of complicated microstructure

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0406U000128

Thesis Registration Form

0406U000128.pdf

Applicant for

Specialization

  • 01.01.03 - Математична фізика

19-12-2005

Specialized Academic Board

Д 64.175.01

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Essay

The thesis deals with harmonic 1- and 2- forms on manifolds of complicated microstructure. The asymptotic behaviour of harmonic 1-forms with given periods on Riemannian surfaces of unboundly increasing genus is studied. The homogenized description of harmonic 1-forms on 4-dimensional pseudo-Riemannian manifolds of complicated microstructure is obtained. The result of homogenization of Cauchy problem for wave equation is obtained. The asymptotic behaviour of the solution of Cauchy problem for Maxwell equations on 4-dimensional space-time manifolds of special structure is investigated. 6156

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