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 Chelyab. Fiz.-Mat. Zh., 2018, Volume 3, Issue 3, Pages 276–294 (Mi chfmj105)

Mathematics

The conjugation problems for some analogues of the equation of longitudinal waves with a discontinuous coefficient

A. I. Grigorieva

North-Eastern Federal University named after M. K. Ammosov

Abstract: It is studied the solvability of conjugation problems for a composite type equation with a discontinuous coefficient. In the first case it is considered the elliptic problem and in the second — an initial-boundary problem. By the method of continuation with respect to a parameter, existence and uniqueness theorems for regular solutions are proved. Also, various examples of the nonuniqueness of the existence of solutions are given, depending on how the discontinuous function behaves in one or another given region.

Keywords: discontinuous coefficient, conjugation problem, regular solution, existence and uniqueness of a solution, method of parameter extension, apriory estimate.

DOI: https://doi.org/10.24411/2500-0101-2018-13302

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Revised: 30.06.2018

Citation: A. I. Grigorieva, “The conjugation problems for some analogues of the equation of longitudinal waves with a discontinuous coefficient”, Chelyab. Fiz.-Mat. Zh., 3:3 (2018), 276–294

Citation in format AMSBIB
\Bibitem{Gri18} \by A.~I.~Grigorieva \paper The conjugation problems for some analogues of the equation of longitudinal waves with a discontinuous coefficient \jour Chelyab. Fiz.-Mat. Zh. \yr 2018 \vol 3 \issue 3 \pages 276--294 \mathnet{http://mi.mathnet.ru/chfmj105} \crossref{https://doi.org/10.24411/2500-0101-2018-13302} \elib{http://elibrary.ru/item.asp?id=35559232}