Geodesic
On a class of nonlocal problems for hyperbolic equations with degeneration of type and order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 137 (2014) no. 4, pp. 22-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Nonlocal problems for the second order hyperbolic model equation were studied in the characteristic area. The type and order of equations degenerate on the same line $ y = 0 $. Nonlocal condition is given by means of fractional integro-differentiation of arbitrary order on the boundary. Nonlocal condition connects fractional derivatives and integrals of the desired solution. For different values of order operators of fractional integro-differentiation within the boundary condition the unique solvability of the considered problems was proved or non-uniqueness of the solution was estimated.
Keywords: nonlocal boundary value problem, fractional integro-differentiation operators, Cauchy problem, second kind Volterra integral equation, Abel integral equation. 
@article{VSGTU_2014_137_4_a2,
     author = {O. A. Repin and S. K. Kumykova},
     title = {On a class of nonlocal problems for hyperbolic equations with degeneration of type and order},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {22--32},
     year = {2014},
     volume = {137},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a2/}
}
TY  - JOUR
AU  - O. A. Repin
AU  - S. K. Kumykova
TI  - On a class of nonlocal problems for hyperbolic equations with degeneration of type and order
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2014
SP  - 22
EP  - 32
VL  - 137
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a2/
LA  - ru
ID  - VSGTU_2014_137_4_a2
ER  - 
%0 Journal Article
%A O. A. Repin
%A S. K. Kumykova
%T On a class of nonlocal problems for hyperbolic equations with degeneration of type and order
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2014
%P 22-32
%V 137
%N 4
%U http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a2/
%G ru
%F VSGTU_2014_137_4_a2
O. A. Repin; S. K. Kumykova. On a class of nonlocal problems for hyperbolic equations with degeneration of type and order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 137 (2014) no. 4, pp. 22-32. http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a2/