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.

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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 
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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/

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