SOLVABILITY OF PROBLEMS OF RECOVERING THE EXTERNAL INFLUENCE IN THE FIRST ORDER HYPERBOLIC EQUATIONS

Kozhanov A.I. Aitzhanov S.E. Zhalgassova K.A.
2022 M. K. Ammosov North-Eastern Federal University

Mathematical Notes of NEFU
2022 #29 Issue 3 42 - 56 pp.

We study the solvability in Sobolev spaces of the problem of recovering the coefficients of the right-hand side, or the external influence, in the first order hyperbolic differential equations. Such problems belong to the class of linear inverse problems for partial differential equations. For the problems under study, we prove the existence and uniqueness theorems for regular solutions (having all generalized in Sobolev’s sense derivatives entering the equation).

existence and uniqueness of solution , first order hyperbolic differential equation , inverse problem , regular solution , unknown external influence

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Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation
Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty, 050040, Kazakhstan
Auezov South Kazakhstan University, 5 Tauke Khan Avenue, Shymkent, 160012, Kazakhstan

Sobolev Institute of Mathematics
Al-Farabi Kazakh National University
Auezov South Kazakhstan University

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