Geodesic
Inverse problem for an equation of mixed parabolic-hyperbolic type with a characteristic line of change
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 4, pp. 607-620

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This study investigates direct and inverse problems for a model equation of mixed parabolic-hyperbolic type. In the direct problem, an analogue of the Tricomi problem is considered for this equation with a characteristic line of type change. The unknown in the inverse problem is a variable coefficient of the lower-order term in the parabolic equation. To determine it relative to the solution defined in the parabolic part of the domain, an integral overdetermination condition is specified. Local theorems of unique solvability of the posed problems in terms of classical solutions are proven.
Keywords: parabolic-hyperbolic equation, characteristic, Green's function, inverse problem, principle of compressed mappings 
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     author = {D. K. Durdiev},
     title = {Inverse problem for an equation of mixed parabolic-hyperbolic type with a characteristic line of change},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {607--620},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2023_27_4_a0/}
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D. K. Durdiev. Inverse problem for an equation of mixed parabolic-hyperbolic type with a characteristic line of change. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 4, pp. 607-620. http://geodesic.mathdoc.fr/item/VSGTU_2023_27_4_a0/