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On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations


Authors: Sh. Sahaev and V. A. Solonnikov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 985-1003
MSC (2010): Primary 45B05
Published electronically: September 21, 2015
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Abstract: The paper is concerned with a linear system of Fredholm-Volterra singular integral equations arising in the study of a linearized initial-boundary value problem of magnetohydrodymnamics for a fluid surrounded by an infinite vacuum region. It is proved that this system is solvable in the class of continuous functions satisfying the Hölder condition with respect to the spatial variables, which yields a classical solution of the problem in question.


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Additional Information

Sh. Sahaev
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: Sahaev@pdmi.ras.ru

V. A. Solonnikov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: solonnik@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1371
Keywords: Fredholm--Volterra singular integral equations, classical solution
Received by editor(s): August 4, 2014
Published electronically: September 21, 2015
Dedicated: Dedicated to Professor G. Grubb on the occasion of her jubilee
Article copyright: © Copyright 2015 American Mathematical Society