Geodesic
Solvability of problems of recovering the external influence in the first order hyperbolic equations
Matematičeskie zametki SVFU, Tome 29 (2022) no. 3, pp. 42-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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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).
Keywords: first order hyperbolic differential equation, inverse problem, unknown external influence, regular solution, existence and uniqueness of solution. 
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     author = {A. I. Kozhanov and S. E. Aitzhanov and K. A. Zhalgassova},
     title = {Solvability of problems of recovering the external influence in the first order hyperbolic equations},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {42--56},
     year = {2022},
     volume = {29},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_3_a3/}
}
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A. I. Kozhanov; S. E. Aitzhanov; K. A. Zhalgassova. Solvability of problems of recovering the external influence in the first order hyperbolic equations. Matematičeskie zametki SVFU, Tome 29 (2022) no. 3, pp. 42-56. http://geodesic.mathdoc.fr/item/SVFU_2022_29_3_a3/