Geodesic
Local and nonlocal value boundary problems for a~third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 21-28

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The existence and uniqueness of local and nonlocal value boundary problems for third-order mixed-type equations with multiple characteristics is proved. Uniqueness of the problem solution is proved with energy-integral method. The existence of the solution is proved with equivalent reduction method to Fredholm integral equations of the second kind with the help of Green's function.
Keywords: local value boundary problem, nonlocal value boundary problem, mixed-type equations, Green's function, Fredholm integral equation. 
@article{VSGTU_2008_2_a2,
     author = {Zh. A. Balkizov},
     title = {Local and nonlocal value boundary problems for a~third-order mixed-type equation equipped with {Tricomi} operator in its hyperbolic part},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {21--28},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2008_2_a2/}
}
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Zh. A. Balkizov. Local and nonlocal value boundary problems for a~third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 21-28. http://geodesic.mathdoc.fr/item/VSGTU_2008_2_a2/