Boundary value problems with nonlocal conditions for hyperbolic systems of equations with two independent variables

V. M. Kyrylych; O. Z. Slyusarchuk

doi:10.30970/ms.53.2.159-180

V. M. Kyrylych Ivan Franko National University of Lviv, Lviv
O. Z. Slyusarchuk Lviv Polytechnic National University, Lviv, Ukraine

DOI: https://doi.org/10.30970/ms.53.2.159-180

Keywords: nonlocal boundary value problem; hyperbolic system; method of characteristics; piecewise smooth coefficients; Volterra-type integral equation; piecewise smooth solution

Abstract

Nonlocal boundary value problems for arbitrary order hyperbolic systems with one spatial variable are considered. A priori estimates for general nonlocal mixed problems for systems with smooth and piecewise smooth coefficients are obtained. The correct solvability of such problems is proved.
Examples of additional conditions necessity are provided.

Author Biographies

V. M. Kyrylych, Ivan Franko National University of Lviv, Lviv

Department of Mechanics and Mathematics, Professor

O. Z. Slyusarchuk, Lviv Polytechnic National University, Lviv, Ukraine

Lviv Polytechnic National University,
Lviv, Ukraine

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