Geodesic
Boundary value problem for mixed type equation of the third order with periodic conditions
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 29-45

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem for the equation of the mixed elliptic-hyperbolic type with nonlocal boundary conditions is viewed. This problem is reduced to the inverse problem for elliptic-hyperbolic equation with unknown right-hand parts. The criterion of the uniqueness is established. The explicit solution is constructed as the sum of orthogonal trigonometric series of the one-dimensional spectral problem eigenfunctions. The argumentation of the series convergence under some restrictions is given. The stability of the solution by the boundary functions is proved.
Keywords: equations of the mixed type of third order, direct and inverse problems, spectral method, uniqueness, stability.
Mots-clés : existense 
@article{VSGTU_2013_3_a2,
     author = {K. B. Sabitov and G. Yu. Udalova},
     title = {Boundary value problem for mixed type equation of the third order with periodic conditions},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {29--45},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a2/}
}
TY  - JOUR
AU  - K. B. Sabitov
AU  - G. Yu. Udalova
TI  - Boundary value problem for mixed type equation of the third order with periodic conditions
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 29
EP  - 45
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a2/
LA  - ru
ID  - VSGTU_2013_3_a2
ER  - 
%0 Journal Article
%A K. B. Sabitov
%A G. Yu. Udalova
%T Boundary value problem for mixed type equation of the third order with periodic conditions
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 29-45
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a2/
%G ru
%F VSGTU_2013_3_a2
K. B. Sabitov; G. Yu. Udalova. Boundary value problem for mixed type equation of the third order with periodic conditions. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2013), pp. 29-45. http://geodesic.mathdoc.fr/item/VSGTU_2013_3_a2/