Počet záznamů: 1

Convergence of the Neumann series in BEM for the Neumann problem of the stokes system

  1. 1.
    0367466 - MU-W 2012 RIV NL eng J - Článek v odborném periodiku
    Medková, Dagmar
    Convergence of the Neumann series in BEM for the Neumann problem of the stokes system.
    Acta Applicandae Mathematicae. Roč. 116, č. 3 (2011), s. 281-304 ISSN 0167-8019
    Grant CEP: GA AV ČR IAA100190804
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: stokes system * Neumann problem * integral equation method
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.899, rok: 2011
    http://www.springerlink.com/content/d73174l507577464/

    A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability of the problem are given. Moreover, it is shown that we can obtain a solution of this integral equation using the successive approximation method. Then the consequences for the direct boundary integral equation method are treated. A solution of the Neumann problem for the Stokes system is the sum of the hydrodynamical single layer potential corresponding to the boundary condition and the hydrodynamical double layer potential corresponding to the trace of the velocity part of the solution. Using boundary behavior of potentials we get an integral equation on the boundary of the domain where the trace of the velocity part of the solution is unknown.
    Trvalý link: http://hdl.handle.net/11104/0202143
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