Open AccessABOUT A TRANSFORMATION OF SCHWARZ PROBLEM
Author(s) -
В. Г. Николаев
Publication year - 2012
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2012-18-6-27-34
Subject(s) - mathematics , transformation (genetics) , schwarz alternating method , uniqueness , reduction (mathematics) , additive schwarz method , dirichlet problem , order (exchange) , matrix (chemical analysis) , dirichlet distribution , pure mathematics , calculus (dental) , algebra over a field , mathematical analysis , boundary value problem , finite element method , geometry , medicine , biochemistry , chemistry , physics , materials science , domain decomposition methods , finance , dentistry , economics , composite material , gene , thermodynamics
We consider the Schwarz problem for vector-valued functions analytic according to Douglis. We prove that under certain conditions on the matrix this problem is reduced to the Dirichlet problem for some equivalent system of second-order PDEs. The reversebility of transformations is proved, and on that ground the theorem of uniqueness is established. A special case when reduction is impossible is also viewed. The examples are given.