On solvability of nonlocal problem for loaded parabolic-hyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 62-69
Voir la notice de l'article provenant de la source Math-Net.Ru
We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.
Keywords:
boundary-value problem, equation of mixed type, operators of fractional integro-differentiation in the Riemann–Liouville sense, generalized operators of fractional integro-differentiation in the M. Saigo sense, Fredholm integral equation of the second kind.
@article{IVM_2018_3_a6,
author = {A. V. Tarasenko},
title = {On solvability of nonlocal problem for loaded parabolic-hyperbolic equation},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {62--69},
publisher = {mathdoc},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2018_3_a6/}
}
A. V. Tarasenko. On solvability of nonlocal problem for loaded parabolic-hyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 62-69. http://geodesic.mathdoc.fr/item/IVM_2018_3_a6/