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, Tome 132 (2013) no. 3, pp. 29-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, Tome 132 (2013) no. 3, pp. 29-45. http://geodesic.mathdoc.fr/item/VSGTU_2013_132_3_a2/

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