Geodesic
Solvability of BVPs for the parabolic-hyperbolic equation with non-linear loaded term
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 2, pp. 133-143

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This work is devoted to prove the existence and uniqueness of solution of BVP with non-local assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation involving Caputo derivatives. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations.
Keywords: Caputo fractional derivatives, loaded equation, integral gluing condition, non-linear integral equation, non-local problem, existence and uniqueness of solution. 
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     title = {Solvability of {BVPs} for the parabolic-hyperbolic equation with non-linear loaded term},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {133--143},
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     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_2_a0/}
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Obidjon Kh. Abdullaev. Solvability of BVPs for the parabolic-hyperbolic equation with non-linear loaded term. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 2, pp. 133-143. http://geodesic.mathdoc.fr/item/JSFU_2021_14_2_a0/