Geodesic
A nonlocal problem for a third order parabolic-hyperbolic equation with a singular coefficient
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 4, pp. 467-481

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Non-classical problem with an integral condition for parabolic-hyperbolic equation of the third order is formulated and studied in this paper. The unique solvability of the problem was proved using the method integral equations. To do this the problem is equivalently reduced to a problem for a parabolic-hyperbolic equation of the second order with an unknown right-hand side. To study the obtained problem the formula of the Cauchy problem for hyperbolic equation with a singular coefficient and a spectral parameter was used. The solution of the first boundary value problem for the Fourier equation was also used.
Keywords: parabolic-hyperbolic equation, integral condition, uniqueness of the solution, existence of the solution
Mots-clés : singular coefficient. 
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     title = {A nonlocal problem for a third order parabolic-hyperbolic equation with a singular coefficient},
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Akhmadjon K. Urinov; Kobiljon S. Khalilov. A nonlocal problem for a third order parabolic-hyperbolic equation with a singular coefficient. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 4, pp. 467-481. http://geodesic.mathdoc.fr/item/JSFU_2022_15_4_a5/